New Upstream Snapshot - r-cran-matrixcalc

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Maintainer email: r-pkg-team@alioth-lists.debian.net
Automatic publish policy: main: push-derived , pristine-tar: push-derived , upstream: push-derived
Last processed: 2023-09-08T13:57 (took 20m10s)
Branch URL: https://salsa.debian.org/r-pkg-team/r-cran-matrixcalc.git -b master (taken from version 1.0.6-1)
Queue position: 125289 (a 52w6d wait)

Ready changes

Summary

Merged new upstream version: 1.0.6+git20210727.1.c45ccce (was: 1.0.6).

Resulting package

Built on 2022-12-20T08:25 (took 10m34s)

The resulting binary packages can be installed (if you have the apt repository enabled) by running one of:

apt install -t fresh-snapshots r-cran-matrixcalc

Lintian Result

r-cran-matrixcalc_1.0.6+git20210727.1.c45ccce-1~jan+nus2.dsc

r-cran-matrixcalc_1.0.6+git20210727.1.c45ccce-1~jan+nus2_all.deb

r-cran-matrixcalc_1.0.6+git20210727.1.c45ccce-1~jan+nus2_amd64.buildinfo

r-cran-matrixcalc_1.0.6+git20210727.1.c45ccce-1~jan+nus2_amd64.changes

Diff

diff --git a/DESCRIPTION b/DESCRIPTION
index c683583..ea7627b 100755
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: matrixcalc
-Version: 1.0-6
-Date: 2022-09-10
+Version: 1.0-5
+Date: 2021-05-27
 Title: Collection of Functions for Matrix Calculations
 Author: Frederick Novomestky <fnovomes@poly.edu>
 Maintainer: S. Thomas Kelly <tomkellygenetics@gmail.com>
@@ -17,8 +17,7 @@ Description: A collection of functions to support matrix calculations
         Lay, D.C. (1995) Linear Algebra: And Its Applications. ISBN 978-0201845563.
 License: GPL (>= 2)
 BugReports: https://github.com/TomKellyGenetics/matrixcalc/issues
-Packaged: 2022-09-14 20:41:38 UTC; tom
+Packaged: 2022-12-20 08:18:32 UTC; root
 Repository: CRAN
-Date/Publication: 2022-09-14 21:20:02 UTC
-RoxygenNote: 7.1.2
+Date/Publication: 2012-09-15 14:22:14
 NeedsCompilation: no
diff --git a/MD5 b/MD5
deleted file mode 100644
index ea7ad1e..0000000
--- a/MD5
+++ /dev/null
@@ -1,122 +0,0 @@
-5fddfc997e504f85a94291150b99522c *DESCRIPTION
-4be87d2e3c549f8c524f6b2eb86399a4 *NAMESPACE
-2c8d8a78f8b955c2f2f586f5bacf3247 *R/D.matrix.R
-c944e010361d98b90fa512d4965c2383 *R/E.matrices.R
-71f6be247b2345ec1b5872466dca2431 *R/H.matrices.R
-bac34a744518cce7b5734850d45c2c0d *R/K.matrix.R
-6bfb2781f2ec3698bfc5bd1ddcfe18b4 *R/L.matrix.R
-27337ba4230b62fca4d790395cabc6c7 *R/N.matrix.R
-d96685a05d885d85e0e6b1dc039c8636 *R/T.matrices.R
-731b97ec42f006705fa4f58c63d58331 *R/commutation.matrix.R
-62d0ea817d89796582fa953f9c1b79f4 *R/creation.matrix.R
-4f5d46a65ee100372c0c80a4b7d0603a *R/direct.prod.R
-1b39be5b4507e9602c51b1896e6d3422 *R/direct.sum.R
-5d17bc6c0d27ee7068d386a44ba72197 *R/duplication.matrix.R
-8402bc1d6f15c51b509a6994f1a479bd *R/elimination.matrix.R
-c24998138a3dd7b1dcc2f407a3b480c6 *R/entrywise.norm.R
-2af94e74841a173131de053da13ab533 *R/fibonacci.matrix.R
-50258bc682374273a28a380dae663d6d *R/frobenius.matrix.R
-b020074d548aa68ce6c9755f3c1b6597 *R/frobenius.norm.R
-53a9d15f46b3e8466f87e99cabb92b5a *R/frobenius.prod.R
-e9c899e4c92acc318be7601edc455274 *R/hadamard.prod.R
-20c120bdd52fdf11e119fd462857c3a2 *R/hankel.matrix.R
-94d010622099c5df6d00a5ee1b44c9be *R/hilbert.matrix.R
-03f9f1cc9600fdca28156874500c17b0 *R/hilbert.schmidt.norm.R
-bfd6ddd08302469dbaccc423d4d5bb7d *R/inf.norm.R
-d76fb3d0f200436c6afd92d564e2beaa *R/is.diagonal.matrix.R
-d6926822047856a2cddfb43accc7d1f9 *R/is.idempotent.matrix.R
-69c3ad7f0dd3faa8bdb8f5bbe87d14c0 *R/is.indefinite.R
-f19a39fd4514178e639f23bde97f57d2 *R/is.negative.definite.R
-d95e8f31b7d26c37d467f3775bd34018 *R/is.negative.semi.definite.R
-585936c334ddb173cb10d2db939ccbcb *R/is.non.singular.matrix.R
-58c2d05f1d185786ce9ae9fe19775007 *R/is.positive.definite.R
-0d022dbd6264554b4c4ddc99a8f11298 *R/is.positive.semi.definite.R
-e564d72c304cf0642a4725a14f6db0c1 *R/is.singular.matrix.R
-a4ec06b010bf211e602b4280f71a0bb1 *R/is.skew.symmetric.matrix.R
-b2802b610ed8ed62f80f9ee033daca6a *R/is.square.matrix.R
-12e88ca7d5a56f3cefe9d9f58b28303d *R/is.symmetric.matrix.R
-907309ee331e787525665baf8d4d7bbb *R/lower.triangle.R
-79db8c243e35db286b07288baa42a79e *R/lu.decomposition.R
-6a041d084671936aeea6dc60f7d03e81 *R/matrix.inverse.R
-8e8317708b130adbc237bdef10a52429 *R/matrix.power.R
-7d534f91782c58f31c0fc0c28a320f4d *R/matrix.rank.R
-3ca0a03e3e14cbb0a1fee4469da0fba0 *R/matrix.trace.R
-50226dcc08883e432a536c5d2e53740c *R/maximum.norm.R
-d64f99922b89078fde55fddb62295d78 *R/one.norm.R
-c2268f4acabb63a19e57c36b86176de3 *R/pascal.matrix.R
-a27bbcb2fcbe235cd7a88af3f84e9cd9 *R/s.R
-b613d92fed28d6f3eb0e7af25dd24996 *R/set.submatrix.R
-60db620761b455d664794429630a6068 *R/shift.down.R
-84fdb4a3e40935401b3c3a7d58f6746a *R/shift.left.R
-207fe5b7689a24f12de2d5c6e90812f3 *R/shift.right.R
-aebd7ca6804ca7d75f1e994bd53f3822 *R/shift.up.R
-f2b024e0a9d6a0681aa925dc1b689193 *R/spectral.norm.R
-8ac6dda72539bbfebcd90167b8e417cc *R/stirling.matrix.R
-5d812285c95d446c8c0403e1798298fa *R/svd.inverse.R
-76f90e460e592bb3aff31e5b30972874 *R/symmetric.pascal.matrix.R
-4b0d3e6ed0f288d2e377680be9865398 *R/toeplitz.matrix.R
-adaba9414c7856677859ee1789cbe572 *R/u.vectors.R
-aa3e0e4259548ec8a43d1b0651fe36af *R/upper.triangle.R
-e4051eb23562f1d7659d03a8a190a262 *R/vandermonde.matrix.R
-5e252bd16e54c9bcb932d6a0c33e521c *R/vec.R
-8cd0039aa5da08f8a764a25aa9706605 *R/vech.R
-f17f9fe5061d3e7438ded85ae05ff90f *man/D.matrix.Rd
-7ecd73b8b0469e84543a2a729e3368d6 *man/E.matrices.Rd
-ece0fc776e80fe178d8aaf69a5fde48f *man/H.matrices.Rd
-1ec8f56a42e5688c29d779eb1366771a *man/K.matrix.Rd
-dd4b8573f995b07a785a1bf9d192ea86 *man/L.matrix.Rd
-3eb45e5f490409c2c0a16ac88f602780 *man/N.matrix.Rd
-8eb201394430f86635023fc6618c8e52 *man/T.matrices.Rd
-41e2921d8c6ec2bcb30a5cda7e519afe *man/commutation.matrix.Rd
-e5a780c7807410a10df16798edaa62d9 *man/creation.matrix.Rd
-4c6cd2d66daae9265f75ccfbbdb1e1b8 *man/direct.prod.Rd
-182f26dcc99da13388a57b3a95167100 *man/direct.sum.Rd
-46d6a71d212e1b4d4dd2fefd7ba8c73c *man/duplication.matrix.Rd
-96c4fe4f2951106350e00ecdc4cbda4d *man/elimination.matrix.Rd
-fd803187d1c7d904c4ad0774f8d4af5d *man/entrywise.norm.Rd
-407ccf707d7e5381e4860bae66490af4 *man/fibonacci.matrix.Rd
-6d6d9424ba31308545a0bc4646ff1306 *man/frobenius.matrix.Rd
-9c220bd48b8647a03af07a1b1e65b958 *man/frobenius.norm.Rd
-3762d52ec2ba465780cf69c0ef735299 *man/frobenius.prod.Rd
-a5610b10c4535fa10fb10b07152bd6b7 *man/hadamard.prod.Rd
-1c5cfcdf203fb6a803433f2a45a4262e *man/hankel.matrix.Rd
-eff91d40920940f352aacf3db5b731d4 *man/hilbert.matrix.Rd
-c1757d64209ab93f178eb4ce9ea308a1 *man/hilbert.schmidt.norm.Rd
-84056ba8a2076501f12d8011bce7ddab *man/inf.norm.Rd
-f049c95092c0e185781c0a5c8dca55ac *man/is.diagonal.matrix.Rd
-e750075c6d7cebe7212a8e871d5ccdc1 *man/is.idempotent.matrix.Rd
-66ead0277a0eb0465f528e6a6413ea45 *man/is.indefinite.Rd
-dfda51ad25fcd20920c2d214d7c2ac44 *man/is.negative.definite.Rd
-4ecde6214f09866673d71617f367c360 *man/is.negative.semi.definite.Rd
-336032c0dca84b270abe70a3f9528dd9 *man/is.non.singular.matrix.Rd
-d983002b402c550424e7de39d515c002 *man/is.positive.definite.Rd
-809d472d0eb36f1e25499ed919a9cbc9 *man/is.positive.semi.definite.Rd
-61d76faf6cf0e32173ba254b43c3a9ed *man/is.singular.matrix.Rd
-cc19c1b6d7e99dac30190fbf2c2319b2 *man/is.skew.symmetric.matrix.Rd
-e0a44a72ef6092f776027f6beb733fc3 *man/is.square.matrix.Rd
-16834db4037d979e5a084785065093bc *man/is.symmetric.matrix.Rd
-1ba1db89a584df8379b8dcfeafcf2edb *man/lower.triangle.Rd
-de76cb0c4aa2b765009074096027f42f *man/lu.decomposition.Rd
-eeaaa7bf444a435a9c008e983739277b *man/matrix.inverse.Rd
-4f18d13b40ac5cc557422bceb8d5f29e *man/matrix.power.Rd
-e4c3e853aa51ec654a3b6b277409c2cc *man/matrix.rank.Rd
-15a7bf0f6e0ec15bc4d42257be52abdd *man/matrix.trace.Rd
-063fbdd190de996f17f7ca996b2c7307 *man/maximum.norm.Rd
-6b71eacdfc47971939e2f4b2f416a3c0 *man/one.norm.Rd
-0396b4b53eaf003cfc3563e442361902 *man/pascal.matrix.Rd
-d95031fcf709832ee0de8a4275a7300c *man/s.Rd
-0d0f2d8d52be9dd7e5859387c7d24ab6 *man/set.submatrix.Rd
-f5fb7a092855b9fd0869ea63b866fc9c *man/shift.down.Rd
-fe70ef6955113afb3ae6e720f25d58aa *man/shift.left.Rd
-ce7f0a6dc0aaf40d301af84baa0c3d0f *man/shift.right.Rd
-c221e34cd76f1833e915625d175a18d3 *man/shift.up.Rd
-1b01fe036063e33f3ca9987ed5ee2230 *man/spectral.norm.Rd
-899e85fc7026d642ce1342c451441537 *man/stirling.matrix.Rd
-cf09112ff8d17dbd566b4966fc805313 *man/svd.inverse.Rd
-fd7be3bbe5d5323ee224ec61ea37180f *man/symmetric.pascal.matrix.Rd
-eae1e19b4b1a8310f661822e6ed2cf3e *man/toeplitz.matrix.Rd
-d41dd5a6db27f12cbb68fd90433070ef *man/u.vectors.Rd
-88533289562cd304f0927691bfcd5bd4 *man/upper.triangle.Rd
-e64da5d9e111155edf077ee79b610226 *man/vandermonde.matrix.Rd
-cf987f9226eb32a8bb064c12192400b2 *man/vec.Rd
-35dc9b5a89f359edb636857fe0e11cf9 *man/vech.Rd
diff --git a/debian/changelog b/debian/changelog
index 4ce7c0c..225d8a9 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -1,3 +1,9 @@
+r-cran-matrixcalc (1.0.6+git20210727.1.c45ccce-1) UNRELEASED; urgency=low
+
+  * New upstream snapshot.
+
+ -- Debian Janitor <janitor@jelmer.uk>  Tue, 20 Dec 2022 08:19:56 -0000
+
 r-cran-matrixcalc (1.0.6-1) unstable; urgency=medium
 
   * Team upload.
diff --git a/man/D.matrix.Rd b/man/D.matrix.Rd
old mode 100644
new mode 100755
index 6212eb4..2f01246
--- a/man/D.matrix.Rd
+++ b/man/D.matrix.Rd
@@ -1,48 +1,48 @@
-\name{D.matrix}
-\alias{D.matrix}
-\title{ Duplication matrix }
-\description{
-  This function constructs the linear transformation D that maps
-  vech(A) to vec(A) when A is a symmetric matrix
-}
-\usage{
-D.matrix(n)
-}
-\arguments{
-  \item{n}{ a positive integer value for the order of the underlying matrix }
-}
-\details{
-  Let \eqn{{\bf{T}}_{i,j}} be an \eqn{n \times n} matrix with 1 in its \eqn{\left( {i,j} \right)} element \eqn{1 \le i,j \le n}.
-  and zeroes elsewhere. These matrices are constructed by the function \code{T.matrices}.  The formula for the
-  transpose of matrix \eqn{\bf{D}} is \eqn{{\bf{D'}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}\;{{\left( {vec\;{{\bf{T}}_{i,j}}} \right)}^\prime }} } }
-  where \eqn{{{{\bf{u}}_{i,j}}}} is the column vector in the order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity
-  matrix for column \eqn{k = \left( {j - 1} \right)n + i - \frac{1}{2}j\left( {j - 1} \right)}.  The function
-  \code{u.vectors} generates these vectors.
-}
-\value{
-  It returns an \eqn{{n^2}\; \times \;\frac{1}{2}n\left( {n + 1} \right)} matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999). \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{T.matrices}},
-  \code{\link{u.vectors}}
-}
-\examples{
-D <- D.matrix( 3 )
-A <- matrix( c( 1, 2, 3,
-                2, 3, 4,
-                3, 4, 5), nrow=3, byrow=TRUE )
-vecA <- vec( A )
-vechA<- vech( A )
-y <- D \%*\% vechA
-print( y )
-print( vecA )
-}
-\keyword{ math }
+\name{D.matrix}
+\alias{D.matrix}
+\title{ Duplication matrix }
+\description{
+  This function constructs the linear transformation D that maps
+  vech(A) to vec(A) when A is a symmetric matrix
+}
+\usage{
+D.matrix(n)
+}
+\arguments{
+  \item{n}{ a positive integer value for the order of the underlying matrix }
+}
+\details{
+  Let \eqn{{\bf{T}}_{i,j}} be an \eqn{n \times n} matrix with 1 in its \eqn{\left( {i,j} \right)} element \eqn{1 \le i,j \le n}.
+  and zeroes elsewhere. These matrices are constructed by the function \code{T.matrices}.  The formula for the
+  transpose of matrix \eqn{\bf{D}} is \eqn{{\bf{D'}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}\;{{\left( {vec\;{{\bf{T}}_{i,j}}} \right)}^\prime }} } }
+  where \eqn{{{{\bf{u}}_{i,j}}}} is the column vector in the order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity
+  matrix for column \eqn{k = \left( {j - 1} \right)n + i - \frac{1}{2}j\left( {j - 1} \right)}.  The function
+  \code{u.vectors} generates these vectors.
+}
+\value{
+  It returns an \eqn{{n^2}\; \times \;\frac{1}{2}n\left( {n + 1} \right)} matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999). \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{T.matrices}},
+  \code{\link{u.vectors}}
+}
+\examples{
+D <- D.matrix( 3 )
+A <- matrix( c( 1, 2, 3,
+                2, 3, 4,
+                3, 4, 5), nrow=3, byrow=TRUE )
+vecA <- vec( A )
+vechA<- vech( A )
+y <- D \%*\% vechA
+print( y )
+print( vecA )
+}
+\keyword{ math }
diff --git a/man/E.matrices.Rd b/man/E.matrices.Rd
old mode 100644
new mode 100755
index d9f23b8..cd889ef
--- a/man/E.matrices.Rd
+++ b/man/E.matrices.Rd
@@ -1,49 +1,49 @@
-\name{E.matrices}
-\alias{E.matrices}
-\title{ List of E Matrices }
-\description{
-  This function constructs and returns a list of lists. The component of
-  each sublist is a square matrix derived from the column vectors of
-  an order n identity matrix.
-}
-\usage{
-E.matrices(n)
-}
-\arguments{
-  \item{n}{ a positive integer for the order of the identity matrix
-}
-}
-\details{
-  Let \eqn{{{\bf{I}}_n} = \lbrack {\begin{array}{cccc}
-  {{{\bf{e}}_1}}&{{{\bf{e}}_2}}& \cdots &{{{\bf{e}}_n}}
-  \end{array}} \rbrack}{} be the order \eqn{n} identity matrix
-  with corresponding unit vectors \eqn{{{{\bf{e}}_i}}} with one in
-  its \eqn{i}th position and zeros elsewhere.  
-  The \eqn{n \times n} matrix \eqn{{{\bf{E}}_{i,j}}} is computed
-  from the unit vectors \eqn{{{{\bf{e}}_i}}} and \eqn{{{{\bf{e}}_j}}}
-  as \eqn{{{\bf{E}}_{i,j}} = {{\bf{e}}_i}\;{{\bf{e'}}_j}}.  These matrices
-  are stored as components in a list of lists.
-}
-\value{
-  A list with \eqn{n} components
-  \item{1 }{A sublist of \eqn{n} components}
-  \item{2 }{A sublist of \eqn{n} components}
- ...
-  \item{n }{A sublist of \eqn{n} components}
-  Each component \eqn{j} of sublist \eqn{i} is a matrix \eqn{{\bf{E}}_{i,j}}
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999). \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  The argument n must be an integer value greater than or equal to 2.
-}
-\examples{
-E <- E.matrices( 3 )
-}
-\keyword{ math }
+\name{E.matrices}
+\alias{E.matrices}
+\title{ List of E Matrices }
+\description{
+  This function constructs and returns a list of lists. The component of
+  each sublist is a square matrix derived from the column vectors of
+  an order n identity matrix.
+}
+\usage{
+E.matrices(n)
+}
+\arguments{
+  \item{n}{ a positive integer for the order of the identity matrix
+}
+}
+\details{
+  Let \eqn{{{\bf{I}}_n} = \left[ {\begin{array}{*{20}{c}}
+  {{{\bf{e}}_1}}&{{{\bf{e}}_2}}& \cdots &{{{\bf{e}}_n}}
+  \end{array}} \right]} be the order \eqn{n} identity matrix
+  with corresponding unit vectors \eqn{{{{\bf{e}}_i}}} with one in
+  its \eqn{i}th position and zeros elsewhere.  
+  The \eqn{n \times n} matrix \eqn{{{\bf{E}}_{i,j}}} is computed
+  from the unit vectors \eqn{{{{\bf{e}}_i}}} and \eqn{{{{\bf{e}}_j}}}
+  as \eqn{{{\bf{E}}_{i,j}} = {{\bf{e}}_i}\;{{\bf{e'}}_j}}.  These matrices
+  are stored as components in a list of lists.
+}
+\value{
+  A list with \eqn{n} components
+  \item{1 }{A sublist of \eqn{n} components}
+  \item{2 }{A sublist of \eqn{n} components}
+ ...
+  \item{n }{A sublist of \eqn{n} components}
+  Each component \eqn{j} of sublist \eqn{i} is a matrix \eqn{{\bf{E}}_{i,j}}
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999). \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  The argument n must be an integer value greater than or equal to 2.
+}
+\examples{
+E <- E.matrices( 3 )
+}
+\keyword{ math }
diff --git a/man/H.matrices.Rd b/man/H.matrices.Rd
old mode 100644
new mode 100755
index 6c97bb8..c0d7563
--- a/man/H.matrices.Rd
+++ b/man/H.matrices.Rd
@@ -1,53 +1,53 @@
-\name{H.matrices}
-\alias{H.matrices}
-\title{ List of H Matrices }
-\description{
-  This function constructs and returns a list of lists. The component of
-  each sublist is derived from column vectors in an order r and order c identity matrix.
-}
-\usage{
-H.matrices(r, c = r)
-}
-\arguments{
-  \item{r}{ a positive integer value for an order r identity matrix }
-  \item{c}{ a positive integer value for an order c identify matrix }
-}
-\details{
-  Let \eqn{{{\bf{I}}_r} = \lbrack {\begin{array}{cccc}
-  {{{\bf{a}}_1}}&{{{\bf{a}}_2}}& \cdots &{{{\bf{a}}_r}}
-  \end{array}} \rbrack} be the order \eqn{r} identity matrix
-  with corresponding unit vectors \eqn{{{{\bf{a}}_i}}} with one in
-  its \eqn{i}th position and zeros elsewhere.  
-  Let \eqn{{{\bf{I}}_c} = \lbrack {\begin{array}{cccc}
-  {{{\bf{b}}_1}}&{{{\bf{b}}_2}}& \cdots &{{{\bf{b}}_c}}
-  \end{array}} \rbrack} be the order \eqn{c} identity matrix
-  with corresponding unit vectors \eqn{{{{\bf{b}}_i}}} with one in
-  its \eqn{i}th position and zeros elsewhere.
-  The \eqn{r \times c} matrix \eqn{{\bf{H}}{}_{i,j} = {{\bf{a}}_i}\;{{\bf{b'}}_j}}
-  is used in the computation of the commutation matrix.
-}
-\value{
-  A list with \eqn{r} components
-  \item{1 }{A sublist of \eqn{c} components}
-  \item{2 }{A sublist of \eqn{c} components}
- ...
-  \item{r }{A sublist of c components}
-  Each component \eqn{j} of sublist \eqn{i} is a matrix \eqn{{\bf{H}}_{i,j}}
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and
-  applications, \emph{The Annals of Statistics}, 7(2), 381-394.
-  
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  The argument n must be an integer value greater than or equal to two.
-}
-\examples{
-H.2.3 <- H.matrices( 2, 3 )
-H.3 <- H.matrices( 3 )
-}
-\keyword{ math }
+\name{H.matrices}
+\alias{H.matrices}
+\title{ List of H Matrices }
+\description{
+  This function constructs and returns a list of lists. The component of
+  each sublist is derived from column vectors in an order r and order c identity matrix.
+}
+\usage{
+H.matrices(r, c = r)
+}
+\arguments{
+  \item{r}{ a positive integer value for an order r identity matrix }
+  \item{c}{ a positive integer value for an order c identify matrix }
+}
+\details{
+  Let \eqn{{{\bf{I}}_r} = \left[ {\begin{array}{*{20}{c}}
+  {{{\bf{a}}_1}}&{{{\bf{a}}_2}}& \cdots &{{{\bf{a}}_r}}
+  \end{array}} \right]} be the order \eqn{r} identity matrix
+  with corresponding unit vectors \eqn{{{{\bf{a}}_i}}} with one in
+  its \eqn{i}th position and zeros elsewhere.  
+  Let \eqn{{{\bf{I}}_c} = \left[ {\begin{array}{*{20}{c}}
+  {{{\bf{b}}_1}}&{{{\bf{b}}_2}}& \cdots &{{{\bf{b}}_c}}
+  \end{array}} \right]} be the order \eqn{c} identity matrix
+  with corresponding unit vectors \eqn{{{{\bf{b}}_i}}} with one in
+  its \eqn{i}th position and zeros elsewhere.
+  The \eqn{r \times c} matrix \eqn{{\bf{H}}{}_{i,j} = {{\bf{a}}_i}\;{{\bf{b'}}_j}}
+  is used in the computation of the commutation matrix.
+}
+\value{
+  A list with \eqn{r} components
+  \item{1 }{A sublist of \eqn{c} components}
+  \item{2 }{A sublist of \eqn{c} components}
+ ...
+  \item{r }{A sublist of c components}
+  Each component \eqn{j} of sublist \eqn{i} is a matrix \eqn{{\bf{H}}_{i,j}}
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and
+  applications, \emph{The Annals of Statistics}, 7(2), 381-394.
+  
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  The argument n must be an integer value greater than or equal to two.
+}
+\examples{
+H.2.3 <- H.matrices( 2, 3 )
+H.3 <- H.matrices( 3 )
+}
+\keyword{ math }
diff --git a/man/K.matrix.Rd b/man/K.matrix.Rd
old mode 100644
new mode 100755
index e877cbc..fb581f7
--- a/man/K.matrix.Rd
+++ b/man/K.matrix.Rd
@@ -1,48 +1,48 @@
-\name{K.matrix}
-\alias{K.matrix}
-\title{ K Matrix }
-\description{
-  This function returns a square matrix of order p = r * c that, 
-  for an r by c matrix A, transforms vec(A) to vec(A') where 
-  prime denotes transpose.
-}
-\usage{
-K.matrix(r, c = r)
-}
-\arguments{
-  \item{r}{ a positive integer row dimension }
-  \item{c}{ a positive integer column dimension }
-}
-\details{
-  The \eqn{r \times c} matrices \eqn{{\bf{H}}{}_{i,j}} constructed
-  by the function \code{H.matrices} are combined using direct product
-  to generate the commutation product with the formula  \eqn{{{\bf{K}}_{r,c}} = \sum\limits_{i = 1}^r {\sum\limits_{j = 1}^c {\left( {{{\bf{H}}_{i,j}} \otimes {{{\bf{H'}}}_{i,j}}} \right)} }}
-}
-\value{
-  An order \eqn{\left( {r\;c} \right)} matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and applications,
-  \emph{The Annals of Statistics}, 7(2), 381-394.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If either argument is less than 2, then the function stops and displays an appropriate error mesage.
-  If either argument is not an integer, then the function stops and displays an appropriate error mesage
-}
-\seealso{
-  \code{\link{H.matrices}}
-}
-\examples{
-K <- K.matrix( 3, 4 )
-A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
-vecA <- vec( A )
-vecAt <- vec( t( A ) )
-y <- K \%*\% vecA
-print( y )
-print( vecAt )
-}
-\keyword{ math }
+\name{K.matrix}
+\alias{K.matrix}
+\title{ K Matrix }
+\description{
+  This function returns a square matrix of order p = r * c that, 
+  for an r by c matrix A, transforms vec(A) to vec(A') where 
+  prime denotes transpose.
+}
+\usage{
+K.matrix(r, c = r)
+}
+\arguments{
+  \item{r}{ a positive integer row dimension }
+  \item{c}{ a positive integer column dimension }
+}
+\details{
+  The \eqn{r \times c} matrices \eqn{{\bf{H}}{}_{i,j}} constructed
+  by the function \code{H.matrices} are combined using direct product
+  to generate the commutation product with the formula  \eqn{{{\bf{K}}_{r,c}} = \sum\limits_{i = 1}^r {\sum\limits_{j = 1}^c {\left( {{{\bf{H}}_{i,j}} \otimes {{{\bf{H'}}}_{i,j}}} \right)} }}
+}
+\value{
+  An order \eqn{\left( {r\;c} \right)} matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and applications,
+  \emph{The Annals of Statistics}, 7(2), 381-394.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If either argument is less than 2, then the function stops and displays an appropriate error mesage.
+  If either argument is not an integer, then the function stops and displays an appropriate error mesage
+}
+\seealso{
+  \code{\link{H.matrices}}
+}
+\examples{
+K <- K.matrix( 3, 4 )
+A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
+vecA <- vec( A )
+vecAt <- vec( t( A ) )
+y <- K \%*\% vecA
+print( y )
+print( vecAt )
+}
+\keyword{ math }
diff --git a/man/L.matrix.Rd b/man/L.matrix.Rd
old mode 100644
new mode 100755
index 5281c8e..9d58556
--- a/man/L.matrix.Rd
+++ b/man/L.matrix.Rd
@@ -1,48 +1,48 @@
-\name{L.matrix}
-\alias{L.matrix}
-\title{ Construct L Matrix }
-\description{
-  This function returns a matrix with n * ( n + 1 ) / 2 rows and N * n columns which
-  for any lower triangular matrix A transforms vec( A ) into vech(A)
-}
-\usage{
-L.matrix(n)
-}
-\arguments{
-  \item{n}{ a positive integer order for the associated matrix A }
-}
-\details{
-  The formula used to compute the L matrix which is also called the elimination matrix is  \eqn{{\bf{L}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}{{\left( {vec\;{{\bf{E}}_{i,j}}} \right)}^\prime }} } }
-  \eqn{{{{\bf{u}}_{i,j}}}} are the \eqn{n \times 1} vectors constructed by the function \code{u.vectors}.
-  \eqn{{{{\bf{E}}_{i,j}}}} are the \eqn{ n \times n} matrices constructed by the function \code{E.matrices}.
-}
-\value{
-  An \eqn{\left[ {\frac{1}{2}n\left( {n + 1} \right)} \right] \times {n^2}} matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument is not an integer, the function displays an error message and stops.
-  If the argument is less than two, the function displays an error message and stops.
-}
-\seealso{
-  \code{\link{elimination.matrix}},
-  \code{\link{E.matrices}},
-  \code{\link{u.vectors}}, 
-}
-\examples{
-L <- L.matrix( 4 )
-A <- lower.triangle( matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE ) )
-vecA <- vec( A )
-vechA <- vech( A )
-y <- L \%*\% vecA
-print( y )
-print( vechA )
-}
-\keyword{ math }
+\name{L.matrix}
+\alias{L.matrix}
+\title{ Construct L Matrix }
+\description{
+  This function returns a matrix with n * ( n + 1 ) / 2 rows and N * n columns which
+  for any lower triangular matrix A transforms vec( A ) into vech(A)
+}
+\usage{
+L.matrix(n)
+}
+\arguments{
+  \item{n}{ a positive integer order for the associated matrix A }
+}
+\details{
+  The formula used to compute the L matrix which is also called the elimination matrix is  \eqn{{\bf{L}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}{{\left( {vec\;{{\bf{E}}_{i,j}}} \right)}^\prime }} } }
+  \eqn{{{{\bf{u}}_{i,j}}}} are the \eqn{n \times 1} vectors constructed by the function \code{u.vectors}.
+  \eqn{{{{\bf{E}}_{i,j}}}} are the \eqn{ n \times n} matrices constructed by the function \code{E.matrices}.
+}
+\value{
+  An \eqn{\left[ {\frac{1}{2}n\left( {n + 1} \right)} \right] \times {n^2}} matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument is not an integer, the function displays an error message and stops.
+  If the argument is less than two, the function displays an error message and stops.
+}
+\seealso{
+  \code{\link{elimination.matrix}},
+  \code{\link{E.matrices}},
+  \code{\link{u.vectors}}, 
+}
+\examples{
+L <- L.matrix( 4 )
+A <- lower.triangle( matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE ) )
+vecA <- vec( A )
+vechA <- vech( A )
+y <- L \%*\% vecA
+print( y )
+print( vechA )
+}
+\keyword{ math }
diff --git a/man/N.matrix.Rd b/man/N.matrix.Rd
old mode 100644
new mode 100755
index fdcc952..04ab97a
--- a/man/N.matrix.Rd
+++ b/man/N.matrix.Rd
@@ -1,41 +1,41 @@
-\name{N.matrix}
-\alias{N.matrix}
-\title{ Construct N Matrix }
-\description{
-  This function returns the order n square matrix that is the sum of
-  an implicit commutation matrix and the order n identity matrix
-  quantity divided by two
-}
-\usage{
-N.matrix(n)
-}
-\arguments{
-  \item{n}{ A positive integer matrix order }
-}
-\details{
-  Let \eqn{{\bf{K}_n}} be the order \eqn{n} implicit commutation matrix (i.e., \eqn{{{\bf{K}}_{n,n}}} ).
-  and \eqn{{{\bf{I}}_n}} the order \eqn{n} identity matrix.  The formula for the matrix is \eqn{{\bf{N}} = \frac{1}{2}\left( {{{\bf{K}}_n} + {{\bf{I}}_n}} \right)}.
-}
-\value{
-  An order \eqn{n} matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument is not an integer, the function displays an error message and stops.
-  If the argument is less than two, the function displays an error message and stops.
-}
-\seealso{
-  \code{\link{K.matrix}}
-}
-\examples{
-N <- N.matrix( 3 )
-print( N )
-}
-\keyword{ math }
+\name{N.matrix}
+\alias{N.matrix}
+\title{ Construct N Matrix }
+\description{
+  This function returns the order n square matrix that is the sum of
+  an implicit commutation matrix and the order n identity matrix
+  quantity divided by two
+}
+\usage{
+N.matrix(n)
+}
+\arguments{
+  \item{n}{ A positive integer matrix order }
+}
+\details{
+  Let \eqn{{\bf{K}_n}} be the order \eqn{n} implicit commutation matrix (i.e., \eqn{{{\bf{K}}_{n,n}}} ).
+  and \eqn{{{\bf{I}}_n}} the order \eqn{n} identity matrix.  The formula for the matrix is \eqn{{\bf{N}} = \frac{1}{2}\left( {{{\bf{K}}_n} + {{\bf{I}}_n}} \right)}.
+}
+\value{
+  An order \eqn{n} matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument is not an integer, the function displays an error message and stops.
+  If the argument is less than two, the function displays an error message and stops.
+}
+\seealso{
+  \code{\link{K.matrix}}
+}
+\examples{
+N <- N.matrix( 3 )
+print( N )
+}
+\keyword{ math }
diff --git a/man/T.matrices.Rd b/man/T.matrices.Rd
old mode 100644
new mode 100755
index 0d2181b..a32990e
--- a/man/T.matrices.Rd
+++ b/man/T.matrices.Rd
@@ -1,49 +1,49 @@
-\name{T.matrices}
-\alias{T.matrices}
-\title{ List of T Matrices }
-\description{
-  This function constructs a list of lists.  The number of components in
-  the high level list is n.  Each of the n components is also a list.
-  Each sub-list has n components each of which is an order n square matrix.
-}
-\usage{
-T.matrices(n)
-}
-\arguments{
-  \item{n}{ a positive integer value for the order of the matrices }
-}
-\details{
-  Let \eqn{{{\bf{E}}_{i,j}}\;i = 1, \ldots ,n\;;\;j = 1, \ldots ,n} 
-  be a representative order \eqn{n} matrix created with function \code{E.matrices}.
-  The order \eqn{n} matrix \eqn{{{\bf{T}}_{i,j}}} is defined as follows
-  \eqn{{{\bf{T}}_{i,j}} = \left\{ {\begin{array}{cc}
-{{{\bf{E}}_{i,j}}}&{i = j}\\
-{{{\bf{E}}_{i,j}} + {{\bf{E}}_{j,i}}}&{i \ne j}
-\end{array}} \right.}
-}
-\value{
-  A list of \eqn{n} components.
-  \item{1 }{A list of \eqn{n} components}
-  \item{2 }{A list of \eqn{n} components}
- ...
-  \item{n }{A list of \eqn{n} components}
-  Each component \eqn{j} of sublist \eqn{i} is a matrix \eqn{{\bf{T}}_{i,j}}
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  The argument n must be an integer value greater than or equal to 2.
-}
-\seealso{
-  \code{\link{E.matrices}}
-}
-\examples{
-T <- T.matrices( 3 )
-}
-\keyword{ math }
+\name{T.matrices}
+\alias{T.matrices}
+\title{ List of T Matrices }
+\description{
+  This function constructs a list of lists.  The number of components in
+  the high level list is n.  Each of the n components is also a list.
+  Each sub-list has n components each of which is an order n square matrix.
+}
+\usage{
+T.matrices(n)
+}
+\arguments{
+  \item{n}{ a positive integer value for the order of the matrices }
+}
+\details{
+  Let \eqn{{{\bf{E}}_{i,j}}\;i = 1, \ldots ,n\;;\;j = 1, \ldots ,n} 
+  be a representative order \eqn{n} matrix created with function \code{E.matrices}.
+  The order \eqn{n} matrix \eqn{{{\bf{T}}_{i,j}}} is defined as follows
+  \eqn{{{\bf{T}}_{i,j}} = \left\{ {\begin{array}{*{20}{c}}
+{{{\bf{E}}_{i,j}}}&{i = j}\\
+{{{\bf{E}}_{i,j}} + {{\bf{E}}_{j,i}}}&{i \ne j}
+\end{array}} \right.}
+}
+\value{
+  A list of \eqn{n} components.
+  \item{1 }{A list of \eqn{n} components}
+  \item{2 }{A list of \eqn{n} components}
+ ...
+  \item{n }{A list of \eqn{n} components}
+  Each component \eqn{j} of sublist \eqn{i} is a matrix \eqn{{\bf{T}}_{i,j}}
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  The argument n must be an integer value greater than or equal to 2.
+}
+\seealso{
+  \code{\link{E.matrices}}
+}
+\examples{
+T <- T.matrices( 3 )
+}
+\keyword{ math }
diff --git a/man/commutation.matrix.Rd b/man/commutation.matrix.Rd
old mode 100644
new mode 100755
index b197ecc..a67bd61
--- a/man/commutation.matrix.Rd
+++ b/man/commutation.matrix.Rd
@@ -1,50 +1,50 @@
-\name{commutation.matrix}
-\alias{commutation.matrix}
-\title{ Commutation matrix for r by c numeric matrices }
-\description{
-  This function returns a square matrix of order p = r * c that, 
-  for an r by c matrix A, transforms
-  vec(A) to vec(A') where prime denotes transpose.
-}
-\usage{
-commutation.matrix(r, c=r)
-}
-\arguments{
-  \item{r}{ a positive integer integer row dimension }
-  \item{c}{ a positive integer integer column dimension }
-}
-\details{
-  This function is a wrapper function that uses the function \code{K.matrix} to do the actual work.
-  The \eqn{r \times c} matrices \eqn{{\bf{H}}{}_{i,j}} constructed
-  by the function \code{H.matrices} are combined using direct product
-  to generate the commutation product with the following formula
-  \eqn{{{\bf{K}}_{r,c}} = \sum\limits_{i = 1}^r {\sum\limits_{j = 1}^c {\left( {{{\bf{H}}_{i,j}} \otimes {{{\bf{H'}}}_{i,j}}} \right)} }}
-}
-\value{
-  An order \eqn{\left( {r\;c} \right)} matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and applications,
-  \emph{The Annals of Statistics}, 7(2), 381-394.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If either argument is less than 2, then the function stops and displays an appropriate error mesage.
-  If either argument is not an integer, then the function stops and displays an appropriate error mesage
-}
-\seealso{
-  \code{\link{H.matrices}},
-  \code{\link{K.matrix}}
-}
-\examples{
-K <- commutation.matrix( 3, 4 )
-A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
-vecA <- vec( A )
-vecAt <- vec( t( A ) )
-print( K \%*\% vecA )
-print( vecAt )
-}
-\keyword{ math }
+\name{commutation.matrix}
+\alias{commutation.matrix}
+\title{ Commutation matrix for r by c numeric matrices }
+\description{
+  This function returns a square matrix of order p = r * c that, 
+  for an r by c matrix A, transforms
+  vec(A) to vec(A') where prime denotes transpose.
+}
+\usage{
+commutation.matrix(r, c=r)
+}
+\arguments{
+  \item{r}{ a positive integer integer row dimension }
+  \item{c}{ a positive integer integer column dimension }
+}
+\details{
+  This function is a wrapper function that uses the function \code{K.matrix} to do the actual work.
+  The \eqn{r \times c} matrices \eqn{{\bf{H}}{}_{i,j}} constructed
+  by the function \code{H.matrices} are combined using direct product
+  to generate the commutation product with the following formula
+  \eqn{{{\bf{K}}_{r,c}} = \sum\limits_{i = 1}^r {\sum\limits_{j = 1}^c {\left( {{{\bf{H}}_{i,j}} \otimes {{{\bf{H'}}}_{i,j}}} \right)} }}
+}
+\value{
+  An order \eqn{\left( {r\;c} \right)} matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and applications,
+  \emph{The Annals of Statistics}, 7(2), 381-394.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If either argument is less than 2, then the function stops and displays an appropriate error mesage.
+  If either argument is not an integer, then the function stops and displays an appropriate error mesage
+}
+\seealso{
+  \code{\link{H.matrices}},
+  \code{\link{K.matrix}}
+}
+\examples{
+K <- commutation.matrix( 3, 4 )
+A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
+vecA <- vec( A )
+vecAt <- vec( t( A ) )
+print( K \%*\% vecA )
+print( vecAt )
+}
+\keyword{ math }
diff --git a/man/creation.matrix.Rd b/man/creation.matrix.Rd
old mode 100644
new mode 100755
index fd9c977..deea828
--- a/man/creation.matrix.Rd
+++ b/man/creation.matrix.Rd
@@ -1,46 +1,46 @@
-\name{creation.matrix}
-\alias{creation.matrix}
-\title{ Creation Matrix }
-\description{
-  This function returns the order n creation matrix, a square matrix with the
-  sequence 1, 2, ..., n - 1 on the sub-diagonal below the principal diagonal.
-}
-\usage{
-creation.matrix(n)
-}
-\arguments{
-  \item{n}{ a positive integer greater than 1 }
-}
-\details{
-  The order \eqn{n} creation matrix is also called the derivation matrix and is
-  used in numerical mathematics and physics. It arises in the solution of linear
-  dynamical systems.  The form of the matrix is 
-  \eqn{\left\lbrack {\begin{array}{cccccc}
-0&0&0& \cdots &0&0\\
-1&0&0& \cdots &0&0\\
-0&2&0& \cdots &0&0\\
-0&0&3& \ddots &0&0\\
- \vdots & \vdots & \vdots & \ddots & \ddots &{}\\
-0&0&0& \cdots &{n - 1}&0
-\end{array}} \right\rbrack}.
-}
-\value{
-  An order \eqn{n} matrix.
-}
-\references{
-  Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats,
-  \emph{American Mathematical Monthly}, March 2001, 108(3), 232-245.
-  
-  Weinberg, S. (1995). \emph{The Quantum Theory of Fields}, Cambridge
-  University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not an integer that is greater than 1, 
-  the function presents an error message and stops.
-}
-\examples{
-H <- creation.matrix( 10 )
-print( H )
-}
-\keyword{ math }
+\name{creation.matrix}
+\alias{creation.matrix}
+\title{ Creation Matrix }
+\description{
+  This function returns the order n creation matrix, a square matrix with the
+  sequence 1, 2, ..., n - 1 on the sub-diagonal below the principal diagonal.
+}
+\usage{
+creation.matrix(n)
+}
+\arguments{
+  \item{n}{ a positive integer greater than 1 }
+}
+\details{
+  The order \eqn{n} creation matrix is also called the derivation matrix and is
+  used in numerical mathematics and physics. It arises in the solution of linear
+  dynamical systems.  The form of the matrix is 
+  \eqn{\left[ {\begin{array}{*{20}{c}}
+0&0&0& \cdots &0&0\\
+1&0&0& \cdots &0&0\\
+0&2&0& \cdots &0&0\\
+0&0&3& \ddots &0&0\\
+ \vdots & \vdots & \vdots & \ddots & \ddots &{}\\
+0&0&0& \cdots &{n - 1}&0
+\end{array}} \right]}.
+}
+\value{
+  An order \eqn{n} matrix.
+}
+\references{
+  Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats,
+  \emph{American Mathematical Monthly}, March 2001, 108(3), 232-245.
+  
+  Weinberg, S. (1995). \emph{The Quantum Theory of Fields}, Cambridge
+  University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not an integer that is greater than 1, 
+  the function presents an error message and stops.
+}
+\examples{
+H <- creation.matrix( 10 )
+print( H )
+}
+\keyword{ math }
diff --git a/man/direct.prod.Rd b/man/direct.prod.Rd
old mode 100644
new mode 100755
index 6001d46..9e9fb23
--- a/man/direct.prod.Rd
+++ b/man/direct.prod.Rd
@@ -1,38 +1,38 @@
-\name{direct.prod}
-\alias{direct.prod}
-\title{ Direct prod of two arrays }
-\description{
-  This function computes the direct product of two arrays.  The arrays can be
-  numerical vectors or matrices.  The result is a matrix.
-}  
-\usage{
-direct.prod( x, y )
-}
-\arguments{
-  \item{x}{ a numeric matrix or vector }
-  \item{y}{ a numeric matrix or vector }
-}
-\details{
-  If either \eqn{\bf{x}} or \eqn{\bf{y}} is a vector, it is converted to a matrix.
-  Suppose that \eqn{\bf{x}} is an \eqn{m \times n} matrix and \eqn{\bf{y}} is an \eqn{ p \times q}
-  matrix. Then, the function returns the matrix \eqn{\left\lbrack {\begin{array}{cccc}
-{{x_{1,1}}\;{\bf{y}}}&{{x_{1,2}}\;{\bf{y}}}& \cdots &{{x_{1,n}}\;{\bf{y}}}\\
-{{x_{2,1}}\;{\bf{y}}}&{{x_{2,2}}\;{\bf{y}}}& \cdots &{{x_{2,n}}\;{\bf{y}}}\\
- \cdots & \cdots & \cdots & \cdots \\
-{{x_{m,1}}\;{\bf{y}}}&{{x_{m,2}}\;{\bf{y}}}& \cdots &{{x_{m,n}}\;{\bf{y}}}
-\end{array}} \right\rbrack}.
-}
-\value{
-  A numeric matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
-\examples{
-x <- matrix( seq( 1, 4 ) )
-y <- matrix( seq( 5, 8 ) )
-print( direct.prod( x, y ) )
-}
-\keyword{ math }
+\name{direct.prod}
+\alias{direct.prod}
+\title{ Direct prod of two arrays }
+\description{
+  This function computes the direct product of two arrays.  The arrays can be
+  numerical vectors or matrices.  The result is a matrix.
+}  
+\usage{
+direct.prod( x, y )
+}
+\arguments{
+  \item{x}{ a numeric matrix or vector }
+  \item{y}{ a numeric matrix or vector }
+}
+\details{
+  If either \eqn{\bf{x}} or \eqn{\bf{y}} is a vector, it is converted to a matrix.
+  Suppose that \eqn{\bf{x}} is an \eqn{m \times n} matrix and \eqn{\bf{y}} is an \eqn{ p \times q}
+  matrix. Then, the function returns the matrix \eqn{\left[ {\begin{array}{*{20}{c}}
+{{x_{1,1}}\;{\bf{y}}}&{{x_{1,2}}\;{\bf{y}}}& \cdots &{{x_{1,n}}\;{\bf{y}}}\\
+{{x_{2,1}}\;{\bf{y}}}&{{x_{2,2}}\;{\bf{y}}}& \cdots &{{x_{2,n}}\;{\bf{y}}}\\
+ \cdots & \cdots & \cdots & \cdots \\
+{{x_{m,1}}\;{\bf{y}}}&{{x_{m,2}}\;{\bf{y}}}& \cdots &{{x_{m,n}}\;{\bf{y}}}
+\end{array}} \right]}.
+}
+\value{
+  A numeric matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
+\examples{
+x <- matrix( seq( 1, 4 ) )
+y <- matrix( seq( 5, 8 ) )
+print( direct.prod( x, y ) )
+}
+\keyword{ math }
diff --git a/man/direct.sum.Rd b/man/direct.sum.Rd
old mode 100644
new mode 100755
index 03401bb..a08a52b
--- a/man/direct.sum.Rd
+++ b/man/direct.sum.Rd
@@ -1,35 +1,35 @@
-\name{direct.sum}
-\alias{direct.sum}
-\title{ Direct sum of two arrays }
-\description{
-  This function computes the direct sum of two arrays.  The arrays can be
-  numerical vectors or matrices.  The result ia the block diagonal matrix.
-}  
-\usage{
-direct.sum( x, y )
-}
-\arguments{
-  \item{x}{ a numeric matrix or vector }
-  \item{y}{ a numeric matrix or vector }
-}
-\value{
-  A numeric matrix.
-}
-\details{
-  If either \eqn{\bf{x}} or y is a vector, it is converted to a matrix.  The result
-  is a block diagonal matrix \eqn{\left\lbrack {\begin{array}{cc}
-   {\bf{x}} & {\bf{0}}  \\
-   {\bf{0}} & {\bf{y}}  \\
-\end{array}} \right\rbrack}.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
-\examples{
-x <- matrix( seq( 1, 4 ) )
-y <- matrix( seq( 5, 8 ) )
-print( direct.sum( x, y ) )
-}
-\keyword{ math }
+\name{direct.sum}
+\alias{direct.sum}
+\title{ Direct sum of two arrays }
+\description{
+  This function computes the direct sum of two arrays.  The arrays can be
+  numerical vectors or matrices.  The result ia the block diagonal matrix.
+}  
+\usage{
+direct.sum( x, y )
+}
+\arguments{
+  \item{x}{ a numeric matrix or vector }
+  \item{y}{ a numeric matrix or vector }
+}
+\value{
+  A numeric matrix.
+}
+\details{
+  If either \eqn{\bf{x}} or y is a vector, it is converted to a matrix.  The result
+  is a block diagonal matrix \eqn{\left[ {\begin{array}{*{20}c}
+   {\bf{x}} & {\bf{0}}  \\
+   {\bf{0}} & {\bf{y}}  \\
+\end{array}} \right]}.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
+\examples{
+x <- matrix( seq( 1, 4 ) )
+y <- matrix( seq( 5, 8 ) )
+print( direct.sum( x, y ) )
+}
+\keyword{ math }
diff --git a/man/duplication.matrix.Rd b/man/duplication.matrix.Rd
old mode 100644
new mode 100755
index 4e53233..9f1ba09
--- a/man/duplication.matrix.Rd
+++ b/man/duplication.matrix.Rd
@@ -1,50 +1,50 @@
-\name{duplication.matrix}
-\alias{duplication.matrix}
-\title{ Duplication matrix for n by n matrices }
-\description{
-  This function returns a matrix with n * n rows and n * ( n + 1 ) / 2 columns
-  that transforms vech(A) to vec(A) where A is a symmetric n by n matrix.
-}
-\usage{
-duplication.matrix(n=1)
-}
-\arguments{
-  \item{n}{ Row and column dimension }
-}
-\details{
-  This function is a wrapper function for the function \code{D.matrix}.
-  Let \eqn{{\bf{T}}_{i,j}} be an \eqn{n \times n} matrix with 1 in its \eqn{\left( {i,j} \right)} element \eqn{1 \le i,j \le n}.
-  and zeroes elsewhere. These matrices are constructed by the function \code{T.matrices}.  The formula for the
-  transpose of matrix \eqn{\bf{D}} is \eqn{{\bf{D'}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}\;{{\left( {vec\;{{\bf{T}}_{i,j}}} \right)}^\prime }} } }
-  where \eqn{{{{\bf{u}}_{i,j}}}} is the column vector in the order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity
-  matrix for column \eqn{k = \left( {j - 1} \right)n + i - \frac{1}{2}j\left( {j - 1} \right)}.  The function
-  \code{u.vectors} generates these vectors.
-}  
-\value{
-  It returns an \eqn{{n^2}\; \times \;\frac{1}{2}n\left( {n + 1} \right)} matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
-\seealso{
-  \code{\link{D.matrix}},
-  \code{\link{vec}},
-  \code{\link{vech}}
-}
-\examples{
-D <- duplication.matrix( 3 )
-A <- matrix( c( 1, 2, 3,
-                2, 3, 4,
-                3, 4, 5), nrow=3, byrow=TRUE )
-vecA <- vec( A )
-vechA<- vech( A )
-y <- D \%*\% vechA
-print( y )
-print( vecA )
-}
-\keyword{ math }
+\name{duplication.matrix}
+\alias{duplication.matrix}
+\title{ Duplication matrix for n by n matrices }
+\description{
+  This function returns a matrix with n * n rows and n * ( n + 1 ) / 2 columns
+  that transforms vech(A) to vec(A) where A is a symmetric n by n matrix.
+}
+\usage{
+duplication.matrix(n=1)
+}
+\arguments{
+  \item{n}{ Row and column dimension }
+}
+\details{
+  This function is a wrapper function for the function \code{D.matrix}.
+  Let \eqn{{\bf{T}}_{i,j}} be an \eqn{n \times n} matrix with 1 in its \eqn{\left( {i,j} \right)} element \eqn{1 \le i,j \le n}.
+  and zeroes elsewhere. These matrices are constructed by the function \code{T.matrices}.  The formula for the
+  transpose of matrix \eqn{\bf{D}} is \eqn{{\bf{D'}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}\;{{\left( {vec\;{{\bf{T}}_{i,j}}} \right)}^\prime }} } }
+  where \eqn{{{{\bf{u}}_{i,j}}}} is the column vector in the order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity
+  matrix for column \eqn{k = \left( {j - 1} \right)n + i - \frac{1}{2}j\left( {j - 1} \right)}.  The function
+  \code{u.vectors} generates these vectors.
+}  
+\value{
+  It returns an \eqn{{n^2}\; \times \;\frac{1}{2}n\left( {n + 1} \right)} matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
+\seealso{
+  \code{\link{D.matrix}},
+  \code{\link{vec}},
+  \code{\link{vech}}
+}
+\examples{
+D <- duplication.matrix( 3 )
+A <- matrix( c( 1, 2, 3,
+                2, 3, 4,
+                3, 4, 5), nrow=3, byrow=TRUE )
+vecA <- vec( A )
+vechA<- vech( A )
+y <- D \%*\% vechA
+print( y )
+print( vecA )
+}
+\keyword{ math }
diff --git a/man/elimination.matrix.Rd b/man/elimination.matrix.Rd
old mode 100644
new mode 100755
index 363f6f7..6c7cf8c
--- a/man/elimination.matrix.Rd
+++ b/man/elimination.matrix.Rd
@@ -1,49 +1,49 @@
-\name{elimination.matrix}
-\alias{elimination.matrix}
-\title{ Elimination matrix for lower triangular matrices }
-\description{
-  This function returns a matrix with n * ( n + 1 ) / 2 rows and N * n columns which
-  for any lower triangular matrix A transforms vec( A ) into vech(A)
-}
-\usage{
-elimination.matrix(n)
-}
-\arguments{
-  \item{n}{ row or column dimension }
-}
-\details{
-  This function is a wrapper function to the function \code{L.matrix}.
-  The formula used to compute the L matrix which is also called the elimination matrix is  \eqn{{\bf{L}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}{{\left( {vec\;{{\bf{E}}_{i,j}}} \right)}^\prime }} } }
-  \eqn{{{{\bf{u}}_{i,j}}}} are the order \eqn{n\left( {n + 1} \right)/2} vectors constructed by the function \code{u.vectors}.
-  \eqn{{{{\bf{E}}_{i,j}}}} are the \eqn{ n \times n} matrices constructed by the function \code{E.matrices}.
-}  
-\value{
-  An \eqn{\left[ {\frac{1}{2}n\left( {n + 1} \right)} \right] \times {n^2}} matrix.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument is not an integer, the function displays an error message and stops.
-  If the argument is less than two, the function displays an error message and stops.
-}
-\seealso{
-  \code{\link{E.matrices}},
-  \code{\link{L.matrix}},
-  \code{\link{u.vectors}}
-}
-\examples{
-L <- elimination.matrix( 4 )
-A <- lower.triangle( matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE ) )
-vecA <- vec( A )
-vechA <- vech( A )
-y <- L \%*\% vecA
-print( y )
-print( vechA )
-}
-\keyword{ math }
+\name{elimination.matrix}
+\alias{elimination.matrix}
+\title{ Elimination matrix for lower triangular matrices }
+\description{
+  This function returns a matrix with n * ( n + 1 ) / 2 rows and N * n columns which
+  for any lower triangular matrix A transforms vec( A ) into vech(A)
+}
+\usage{
+elimination.matrix(n)
+}
+\arguments{
+  \item{n}{ row or column dimension }
+}
+\details{
+  This function is a wrapper function to the function \code{L.matrix}.
+  The formula used to compute the L matrix which is also called the elimination matrix is  \eqn{{\bf{L}} = \sum\limits_{j = 1}^n {\sum\limits_{i = j}^n {{{\bf{u}}_{i,j}}{{\left( {vec\;{{\bf{E}}_{i,j}}} \right)}^\prime }} } }
+  \eqn{{{{\bf{u}}_{i,j}}}} are the order \eqn{n\left( {n + 1} \right)/2} vectors constructed by the function \code{u.vectors}.
+  \eqn{{{{\bf{E}}_{i,j}}}} are the \eqn{ n \times n} matrices constructed by the function \code{E.matrices}.
+}  
+\value{
+  An \eqn{\left[ {\frac{1}{2}n\left( {n + 1} \right)} \right] \times {n^2}} matrix.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument is not an integer, the function displays an error message and stops.
+  If the argument is less than two, the function displays an error message and stops.
+}
+\seealso{
+  \code{\link{E.matrices}},
+  \code{\link{L.matrix}},
+  \code{\link{u.vectors}}
+}
+\examples{
+L <- elimination.matrix( 4 )
+A <- lower.triangle( matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE ) )
+vecA <- vec( A )
+vechA <- vech( A )
+y <- L \%*\% vecA
+print( y )
+print( vechA )
+}
+\keyword{ math }
diff --git a/man/entrywise.norm.Rd b/man/entrywise.norm.Rd
old mode 100644
new mode 100755
index e19b203..7ca2efa
--- a/man/entrywise.norm.Rd
+++ b/man/entrywise.norm.Rd
@@ -1,46 +1,46 @@
-\name{entrywise.norm}
-\alias{entrywise.norm}
-\title{ Compute the entrywise norm of a matrix }
-\description{
-  This function returns the \eqn{\left\| {\bf{x}} \right\|_p } norm of the matrix \eqn{{\mathbf{x}}}.
-}
-\usage{
-entrywise.norm(x,p)
-}
-\arguments{
-  \item{x}{  a numeric vector or matrix }
-  \item{p}{  a real value for the power }
-}
-\details{
-  Let \eqn{{\bf{x}}} be an \eqn{m \times n} numeric matrix.
-  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_p  = \left( {\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\left| {x_{i,j} } \right|^p } } } \right)^{{1 \mathord{\left/
- {\vphantom {1 p}} \right.
- } p}}}.
-}
-\value{
-  A numeric value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
-  Hopkins University Press.
-
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\note{
-  If argument x is not numeric, the function displays an error message and terminates.
-  If argument x is neither a matrix nor a vector, the function displays an error message and terminates.
-  If argument p is zero, the function displays an error message and terminates.
-}  
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{one.norm}},
-  \code{\link{inf.norm}}
-}
-\examples{
-A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
-print( entrywise.norm( A, 2 ) )
-}
-\keyword{ math }
+\name{entrywise.norm}
+\alias{entrywise.norm}
+\title{ Compute the entrywise norm of a matrix }
+\description{
+  This function returns the \eqn{\left\| {\bf{x}} \right\|_p } norm of the matrix \eqn{{\mathbf{x}}}.
+}
+\usage{
+entrywise.norm(x,p)
+}
+\arguments{
+  \item{x}{  a numeric vector or matrix }
+  \item{p}{  a real value for the power }
+}
+\details{
+  Let \eqn{{\bf{x}}} be an \eqn{m \times n} numeric matrix.
+  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_p  = \left( {\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\left| {x_{i,j} } \right|^p } } } \right)^{{1 \mathord{\left/
+ {\vphantom {1 p}} \right.
+ \kern-\nulldelimiterspace} p}}}.
+}
+\value{
+  A numeric value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
+  Hopkins University Press.
+
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\note{
+  If argument x is not numeric, the function displays an error message and terminates.
+  If argument x is neither a matrix nor a vector, the function displays an error message and terminates.
+  If argument p is zero, the function displays an error message and terminates.
+}  
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{one.norm}},
+  \code{\link{inf.norm}}
+}
+\examples{
+A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
+print( entrywise.norm( A, 2 ) )
+}
+\keyword{ math }
diff --git a/man/fibonacci.matrix.Rd b/man/fibonacci.matrix.Rd
old mode 100644
new mode 100755
index 628e5bc..fbaa37e
--- a/man/fibonacci.matrix.Rd
+++ b/man/fibonacci.matrix.Rd
@@ -1,39 +1,39 @@
-\name{fibonacci.matrix}
-\alias{fibonacci.matrix}
-\title{ Fibonacci Matrix }
-\description{
-  This function constructs the order n + 1 square Fibonacci matrix
-  which is derived from a Fibonacci sequence.
-}
-\usage{
-fibonacci.matrix(n)
-}
-\arguments{
-  \item{n}{ a positive integer value }
-}
-\details{
-  Let \eqn{\left\{ {{f_0},\;{f_1},\; \ldots ,\;{f_n}} \right\}} be the
-  set of \eqn{ n + 1} Fibonacci numbers where \eqn{{f_0} = {f_1} = 1}
-  and \eqn{{f_j} = {f_{j - 1}} + {f_{j - 2}},\quad 2 \le j \le n}.  The
-  order \eqn{n + 1} Fibonacci matrix \eqn{{\bf{F}}} has as typical element
-  \eqn{{F_{i,j}} = \left\{ {\begin{array}{cc}
-{{f_{i - j + 1}}}&{i - j + 1 \ge 0}\\
-0&{i - j + 1 < 0}
-\end{array}} \right.}.
-}
-\value{
-  An order \eqn{n + 1} matrix
-}
-\references{
-  Zhang, Z. and J. Wang (2006). Bernoulli matrix and its algebraic properties,
-  \emph{Discrete Applied Nathematics}, 154, 1622-1632.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not a positive integer, the function presents an error message and stops.
-}
-\examples{
-F <- fibonacci.matrix( 10 )
-print( F )
-}
-\keyword{ math }
+\name{fibonacci.matrix}
+\alias{fibonacci.matrix}
+\title{ Fibonacci Matrix }
+\description{
+  This function constructs the order n + 1 square Fibonacci matrix
+  which is derived from a Fibonacci sequence.
+}
+\usage{
+fibonacci.matrix(n)
+}
+\arguments{
+  \item{n}{ a positive integer value }
+}
+\details{
+  Let \eqn{\left\{ {{f_0},\;{f_1},\; \ldots ,\;{f_n}} \right\}} be the
+  set of \eqn{ n + 1} Fibonacci numbers where \eqn{{f_0} = {f_1} = 1}
+  and \eqn{{f_j} = {f_{j - 1}} + {f_{j - 2}},\quad 2 \le j \le n}.  The
+  order \eqn{n + 1} Fibonacci matrix \eqn{{\bf{F}}} has as typical element
+  \eqn{{F_{i,j}} = \left\{ {\begin{array}{*{20}{c}}
+{{f_{i - j + 1}}}&{i - j + 1 \ge 0}\\
+0&{i - j + 1 < 0}
+\end{array}} \right.}.
+}
+\value{
+  An order \eqn{n + 1} matrix
+}
+\references{
+  Zhang, Z. and J. Wang (2006). Bernoulli matrix and its algebraic properties,
+  \emph{Discrete Applied Nathematics}, 154, 1622-1632.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not a positive integer, the function presents an error message and stops.
+}
+\examples{
+F <- fibonacci.matrix( 10 )
+print( F )
+}
+\keyword{ math }
diff --git a/man/frobenius.matrix.Rd b/man/frobenius.matrix.Rd
old mode 100644
new mode 100755
index 240c616..a1fbfec
--- a/man/frobenius.matrix.Rd
+++ b/man/frobenius.matrix.Rd
@@ -1,42 +1,42 @@
-\name{frobenius.matrix}
-\alias{frobenius.matrix}
-\title{ Frobenius Matrix }
-\description{
-  This function returns an order n Frobenius matrix that is useful
-  in numerical mathematics.
-}
-\usage{
-frobenius.matrix(n)
-}
-\arguments{
-  \item{n}{  a positive integer value greater than 1}
-}
-\details{
-  The Frobenius matrix is also called the companion matrix.  It arises
-  in the solution of systems of linear first order differential equations.
-  The formula for the order \eqn{n} Frobenius matrix is \eqn{{\bf{F}} = 
-\left\lbrack {\begin{array}{ccccc}0&0& \cdots &0&{{{\left( { - 1} \right)}^{n - 1}}
-\left( {\begin{array}{ccccc}n\\0\end{array}} \right)}\\1&0& \cdots &0&{{{\left( { - 1} \right)}^{n - 2}}
-\left( {\begin{array}{ccccc}n\\1\end{array}} \right)}\\0&1& \ddots &0&{{{\left( { - 1} \right)}^{n - 3}}
-\left( {\begin{array}{ccccc}n\\2\end{array}} \right)}\\ \vdots & \vdots & \ddots & \vdots & \vdots \\0&0& \cdots &1&{{{\left( { - 1} \right)}^0}
-\left( {\begin{array}{ccccc}n\\{n - 1}\end{array}} 
-\right)}\end{array}} 
-\right\rbrack}.
-}
-\value{
-  An order \eqn{n} matrix
-}
-\references{
-  Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats,
-  \emph{American Mathematical Monthly}, March 2001, 108(3), 232-245.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not a positive integer that is greater than 1, 
-  the function presents an error message and stops.
-}
-\examples{
-F <- frobenius.matrix( 10 )
-print( F )
-}
-\keyword{ math }
+\name{frobenius.matrix}
+\alias{frobenius.matrix}
+\title{ Frobenius Matrix }
+\description{
+  This function returns an order n Frobenius matrix that is useful
+  in numerical mathematics.
+}
+\usage{
+frobenius.matrix(n)
+}
+\arguments{
+  \item{n}{  a positive integer value greater than 1}
+}
+\details{
+  The Frobenius matrix is also called the companion matrix.  It arises
+  in the solution of systems of linear first order differential equations.
+  The formula for the order \eqn{n} Frobenius matrix is \eqn{{\bf{F}} = 
+\left[ {\begin{array}{*{20}{c}}0&0& \cdots &0&{{{\left( { - 1} \right)}^{n - 1}}
+\left( {\begin{array}{*{20}{c}}n\\0\end{array}} \right)}\\1&0& \cdots &0&{{{\left( { - 1} \right)}^{n - 2}}
+\left( {\begin{array}{*{20}{c}}n\\1\end{array}} \right)}\\0&1& \ddots &0&{{{\left( { - 1} \right)}^{n - 3}}
+\left( {\begin{array}{*{20}{c}}n\\2\end{array}} \right)}\\ \vdots & \vdots & \ddots & \vdots & \vdots \\0&0& \cdots &1&{{{\left( { - 1} \right)}^0}
+\left( {\begin{array}{*{20}{c}}n\\{n - 1}\end{array}} 
+\right)}\end{array}} 
+\right]}.
+}
+\value{
+  An order \eqn{n} matrix
+}
+\references{
+  Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats,
+  \emph{American Mathematical Monthly}, March 2001, 108(3), 232-245.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not a positive integer that is greater than 1, 
+  the function presents an error message and stops.
+}
+\examples{
+F <- frobenius.matrix( 10 )
+print( F )
+}
+\keyword{ math }
diff --git a/man/frobenius.norm.Rd b/man/frobenius.norm.Rd
old mode 100644
new mode 100755
index 1b6a2be..8950c23
--- a/man/frobenius.norm.Rd
+++ b/man/frobenius.norm.Rd
@@ -1,37 +1,37 @@
-\name{frobenius.norm}
-\alias{frobenius.norm}
-\title{ Compute the Frobenius norm of a matrix }
-\description{
-  This function returns the Frobenius norm of the matrix \eqn{{\mathbf{x}}}.
-}
-\usage{
-frobenius.norm(x)
-}
-\arguments{
-  \item{x}{  a numeric vector or matrix }
-}
-\details{
-  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_2}.
-  Note that this is the entrywise norm with exponent 2.
-}
-\value{
-  A numeric value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
-  Hopkins University Press.
-
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{entrywise.norm}}
-}
-\examples{
-A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
-print( frobenius.norm( A ) )
-}
-\keyword{ math }
+\name{frobenius.norm}
+\alias{frobenius.norm}
+\title{ Compute the Frobenius norm of a matrix }
+\description{
+  This function returns the Frobenius norm of the matrix \eqn{{\mathbf{x}}}.
+}
+\usage{
+frobenius.norm(x)
+}
+\arguments{
+  \item{x}{  a numeric vector or matrix }
+}
+\details{
+  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_2}.
+  Note that this is the entrywise norm with exponent 2.
+}
+\value{
+  A numeric value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
+  Hopkins University Press.
+
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{entrywise.norm}}
+}
+\examples{
+A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
+print( frobenius.norm( A ) )
+}
+\keyword{ math }
diff --git a/man/frobenius.prod.Rd b/man/frobenius.prod.Rd
old mode 100644
new mode 100755
index ae10d6e..fa20a28
--- a/man/frobenius.prod.Rd
+++ b/man/frobenius.prod.Rd
@@ -1,43 +1,43 @@
-\name{frobenius.prod}
-\alias{frobenius.prod}
-\title{ Frobenius innter product of matrices }
-\description{
-  This function returns the Fronbenius inner product of two matrices, x and y, with the same row and column dimensions.
-}
-\usage{
-frobenius.prod(x, y)
-}
-\arguments{
-  \item{x}{ a numeric matrix or vector object }
-  \item{y}{ a numeric matrix or vector object }
-}
-\details{
-  The Frobenius inner product is the element-by-element sum of 
-  the Hadamard or Shur product of two numeric matrices.  Let \eqn{{\bf{x}}} and
-  \eqn{{\bf{y}}} be two \eqn{m \times n} matrices.  Then Frobenious inner product
-  is computed as \eqn{\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {x_{i,j} \;y_{i,j} } } }.
-}
-\value{
-  A numeric value.
-}
-\references{
-  Styan, G. P. H. (1973). Hadamard Products and Multivariate Statistical Analysis,
-  \emph{Linear Algebra and Its Applications}, Elsevier, 6, 217-240.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{hadamard.prod}}
-}
-\note{
-  The function converts vectors to matrices if necessary.
-  The function stops running if x or y is not numeric and an error message is displayed.
-  The function also stops running if x and y do not have the same row and column dimensions and an error mesage
-  is displayed.
-}
-\examples{
-x <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
-y <- matrix( c( 2, 4, 6, 8 ), nrow=2, byrow=TRUE )
-z <- frobenius.prod( x, y )
-print( z )
-}
-\keyword{ math }
+\name{frobenius.prod}
+\alias{frobenius.prod}
+\title{ Frobenius innter product of matrices }
+\description{
+  This function returns the Fronbenius inner product of two matrices, x and y, with the same row and column dimensions.
+}
+\usage{
+frobenius.prod(x, y)
+}
+\arguments{
+  \item{x}{ a numeric matrix or vector object }
+  \item{y}{ a numeric matrix or vector object }
+}
+\details{
+  The Frobenius inner product is the element-by-element sum of 
+  the Hadamard or Shur product of two numeric matrices.  Let \eqn{{\bf{x}}} and
+  \eqn{{\bf{y}}} be two \eqn{m \times n} matrices.  Then Frobenious inner product
+  is computed as \eqn{\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {x_{i,j} \;y_{i,j} } } }.
+}
+\value{
+  A numeric value.
+}
+\references{
+  Styan, G. P. H. (1973). Hadamard Products and Multivariate Statistical Analysis,
+  \emph{Linear Algebra and Its Applications}, Elsevier, 6, 217-240.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{hadamard.prod}}
+}
+\note{
+  The function converts vectors to matrices if necessary.
+  The function stops running if x or y is not numeric and an error message is displayed.
+  The function also stops running if x and y do not have the same row and column dimensions and an error mesage
+  is displayed.
+}
+\examples{
+x <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
+y <- matrix( c( 2, 4, 6, 8 ), nrow=2, byrow=TRUE )
+z <- frobenius.prod( x, y )
+print( z )
+}
+\keyword{ math }
diff --git a/man/hadamard.prod.Rd b/man/hadamard.prod.Rd
old mode 100644
new mode 100755
index 4e523bd..771ad25
--- a/man/hadamard.prod.Rd
+++ b/man/hadamard.prod.Rd
@@ -1,48 +1,48 @@
-\name{hadamard.prod}
-\alias{hadamard.prod}
-\title{ Hadamard product of two matrices }
-\description{
-  This function returns the Hadamard or Shur product of two matrices, x and y, that have the same row and
-  column dimensions.
-}
-\usage{
-hadamard.prod(x, y)
-}
-\arguments{
-  \item{x}{ a numeric matrix or vector object }
-  \item{y}{ a numeric matrix or vector object }
-}
-\details{
-  The Hadamard product is an element-by-element product of the two matrices. Let \eqn{{\bf{x}}} 
-  and \eqn{{\bf{x}}} be two \eqn{m \times n} numeric matrices.  The Hadamard product is \eqn{{\bf{x}}\, \circ \,{\bf{y}} = \left\lbrack {\begin{array}{cccc}
-{{x_{1,1}}\,{y_{1,1}}}&{{x_{1,2}}\,{y_{1,2}}}& \cdots &{{x_{1,n}}\,{y_{1,n}}}\\
-{{x_{2,1}}\,{y_{121}}}&{{x_{2,2}}\,{y_{2,2}}}& \cdots &{{x_{2,n}}\,{y_{2,n}}}\\
- \cdots & \cdots & \cdots & \cdots \\
-{{x_{m,1}}\,{y_{m,1}}}&{{x_{m,2}}\,{y_{m,2}}}& \cdots &{{x_{m,n}}\,{y_{m,n}}}
-\end{array}} \right\rbrack}.
-  It uses the * operation in R.
-}
-\value{
-  A matrix.
-}
-\references{
-  Hadamard, J (1983). Resolution d'une question relative aux determinants, \emph{Bulletin des Sciences
-  Mathematiques}, 17, 240-246.
-  
-  Styan, G. P. H. (1973). Hadamard Products and Multivariate Statistical Analysis,
-  \emph{Linear Algebra and Its Applications}, Elsevier, 6, 217-240.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  The function converts vectors to matrices if necessary.
-  The function stops running if x or y is not numeric and an error message is displayed.
-  The function also stops running if x and y do not have the same row and column dimensions and an error mesage
-  is displayed.
-}
-\examples{
-x <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
-y <- matrix( c( 2, 4, 6, 8 ), nrow=2, byrow=TRUE )
-z <- hadamard.prod( x, y )
-print( z )
-}
-\keyword{ math }
+\name{hadamard.prod}
+\alias{hadamard.prod}
+\title{ Hadamard product of two matrices }
+\description{
+  This function returns the Hadamard or Shur product of two matrices, x and y, that have the same row and
+  column dimensions.
+}
+\usage{
+hadamard.prod(x, y)
+}
+\arguments{
+  \item{x}{ a numeric matrix or vector object }
+  \item{y}{ a numeric matrix or vector object }
+}
+\details{
+  The Hadamard product is an element-by-element product of the two matrices. Let \eqn{{\bf{x}}} 
+  and \eqn{{\bf{x}}} be two \eqn{m \times n} numeric matrices.  The Hadamard product is \eqn{{\bf{x}}\, \circ \,{\bf{y}} = \left[ {\begin{array}{*{20}{c}}
+{{x_{1,1}}\,{y_{1,1}}}&{{x_{1,2}}\,{y_{1,2}}}& \cdots &{{x_{1,n}}\,{y_{1,n}}}\\
+{{x_{2,1}}\,{y_{121}}}&{{x_{2,2}}\,{y_{2,2}}}& \cdots &{{x_{2,n}}\,{y_{2,n}}}\\
+ \cdots & \cdots & \cdots & \cdots \\
+{{x_{m,1}}\,{y_{m,1}}}&{{x_{m,2}}\,{y_{m,2}}}& \cdots &{{x_{m,n}}\,{y_{m,n}}}
+\end{array}} \right]}.
+  It uses the * operation in R.
+}
+\value{
+  A matrix.
+}
+\references{
+  Hadamard, J (1983). Resolution d'une question relative aux determinants, \emph{Bulletin des Sciences
+  Mathematiques}, 17, 240-246.
+  
+  Styan, G. P. H. (1973). Hadamard Products and Multivariate Statistical Analysis,
+  \emph{Linear Algebra and Its Applications}, Elsevier, 6, 217-240.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  The function converts vectors to matrices if necessary.
+  The function stops running if x or y is not numeric and an error message is displayed.
+  The function also stops running if x and y do not have the same row and column dimensions and an error mesage
+  is displayed.
+}
+\examples{
+x <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
+y <- matrix( c( 2, 4, 6, 8 ), nrow=2, byrow=TRUE )
+z <- hadamard.prod( x, y )
+print( z )
+}
+\keyword{ math }
diff --git a/man/hankel.matrix.Rd b/man/hankel.matrix.Rd
old mode 100644
new mode 100755
index 8f6c7f2..29e4a6b
--- a/man/hankel.matrix.Rd
+++ b/man/hankel.matrix.Rd
@@ -1,38 +1,38 @@
-\name{hankel.matrix}
-\alias{hankel.matrix}
-\title{ Hankel Matrix }
-\description{
-  This function constructs an order n Hankel matrix from the values in
-  the order n vector x.  Each row of the matrix is a circular shift of
-  the values in the previous row.
-}
-\usage{
-hankel.matrix(n, x)
-}
-\arguments{
-  \item{n}{ a positive integer value for order of matrix greater than 1 }
-  \item{x}{ a vector of values used to construct the matrix }
-}
-\details{
-  A Hankel matrix is a square matrix with constant skew diagonals.
-  The determinant of a Hankel matrix is called a catalecticant.
-  Hankel matrices are formed when the hidden Mark model is sought
-  from a given sequence of data.
-}
-\value{
-  An order \eqn{n} matrix.
-}
-\references{
-  Power, S. C. (1982). \emph{Hankel Operators on Hilbert Spaces}, Research
-  notes in mathematics, Series 64, Pitman Publishing.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not a positive integer, the function presents an error message and stops.
-  If the length of x is less than n, the function presents an error message and stops.
-}
-\examples{
-H <- hankel.matrix( 4, seq( 1, 7 ) )
-print( H )
-}
-\keyword{ math }
+\name{hankel.matrix}
+\alias{hankel.matrix}
+\title{ Hankel Matrix }
+\description{
+  This function constructs an order n Hankel matrix from the values in
+  the order n vector x.  Each row of the matrix is a circular shift of
+  the values in the previous row.
+}
+\usage{
+hankel.matrix(n, x)
+}
+\arguments{
+  \item{n}{ a positive integer value for order of matrix greater than 1 }
+  \item{x}{ a vector of values used to construct the matrix }
+}
+\details{
+  A Hankel matrix is a square matrix with constant skew diagonals.
+  The determinant of a Hankel matrix is called a catalecticant.
+  Hankel matrices are formed when the hidden Mark model is sought
+  from a given sequence of data.
+}
+\value{
+  An order \eqn{n} matrix.
+}
+\references{
+  Power, S. C. (1982). \emph{Hankel Operators on Hilbert Spaces}, Research
+  notes in mathematics, Series 64, Pitman Publishing.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not a positive integer, the function presents an error message and stops.
+  If the length of x is less than n, the function presents an error message and stops.
+}
+\examples{
+H <- hankel.matrix( 4, seq( 1, 7 ) )
+print( H )
+}
+\keyword{ math }
diff --git a/man/hilbert.matrix.Rd b/man/hilbert.matrix.Rd
old mode 100644
new mode 100755
index 0345205..c93e2de
--- a/man/hilbert.matrix.Rd
+++ b/man/hilbert.matrix.Rd
@@ -1,35 +1,35 @@
-\name{hilbert.matrix}
-\alias{hilbert.matrix}
-\title{ Hilbert matrices }
-\description{
-  This function returns an n by n Hilbert matrix.
-}
-\usage{
-hilbert.matrix(n)
-}
-\arguments{
-  \item{n}{ Order of the Hilbert matrix }
-}
-\details{
-  A Hilbert matrix is an order \eqn{n} square matrix of unit fractions with elements 
-  defined as \eqn{H_{i,j}  = {1 \mathord{\left/
- {\vphantom {1 {\left( {i + j - 1} \right)}}} \right.
- } {\left( {i + j - 1} \right)}}}.
-}
-\value{
-  A matrix.
-}
-\references{
-  Hilbert, David (1894). Ein Beitrag zur Theorie des Legendre schen Polynoms,
-  \emph{Acta Mathematica}, Springer, Netherlands, 18, 155-159.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument is less than or equal to zero, the function displays an error message and stops.
-  If the argument is not an integer, the function displays an error message and stops.
-}
-\examples{
-H <- hilbert.matrix( 4 )
-print( H )
-}
-\keyword{ math }
+\name{hilbert.matrix}
+\alias{hilbert.matrix}
+\title{ Hilbert matrices }
+\description{
+  This function returns an n by n Hilbert matrix.
+}
+\usage{
+hilbert.matrix(n)
+}
+\arguments{
+  \item{n}{ Order of the Hilbert matrix }
+}
+\details{
+  A Hilbert matrix is an order \eqn{n} square matrix of unit fractions with elements 
+  defined as \eqn{H_{i,j}  = {1 \mathord{\left/
+ {\vphantom {1 {\left( {i + j - 1} \right)}}} \right.
+ \kern-\nulldelimiterspace} {\left( {i + j - 1} \right)}}}.
+}
+\value{
+  A matrix.
+}
+\references{
+  Hilbert, David (1894). Ein Beitrag zur Theorie des Legendre schen Polynoms,
+  \emph{Acta Mathematica}, Springer, Netherlands, 18, 155-159.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument is less than or equal to zero, the function displays an error message and stops.
+  If the argument is not an integer, the function displays an error message and stops.
+}
+\examples{
+H <- hilbert.matrix( 4 )
+print( H )
+}
+\keyword{ math }
diff --git a/man/hilbert.schmidt.norm.Rd b/man/hilbert.schmidt.norm.Rd
old mode 100644
new mode 100755
index dcec748..5108a6b
--- a/man/hilbert.schmidt.norm.Rd
+++ b/man/hilbert.schmidt.norm.Rd
@@ -1,37 +1,37 @@
-\name{hilbert.schmidt.norm}
-\alias{hilbert.schmidt.norm}
-\title{ Compute the Hilbert-Schmidt norm of a matrix }
-\description{
-  This function returns the Hilbert-Schmidt norm of the matrix \eqn{{\mathbf{x}}}.
-}
-\usage{
-hilbert.schmidt.norm(x)
-}
-\arguments{
-  \item{x}{  a numeric vector or matrix }
-}
-\details{
-  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_2}.
-  This is merely the entrywise norm with exponent 2.
-}
-\value{
-  A numeric value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
-  Hopkins University Press.
-
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{entrywise.norm}}
-}
-\examples{
-A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
-print( hilbert.schmidt.norm( A ) )
-}
-\keyword{ math }
+\name{hilbert.schmidt.norm}
+\alias{hilbert.schmidt.norm}
+\title{ Compute the Hilbert-Schmidt norm of a matrix }
+\description{
+  This function returns the Hilbert-Schmidt norm of the matrix \eqn{{\mathbf{x}}}.
+}
+\usage{
+hilbert.schmidt.norm(x)
+}
+\arguments{
+  \item{x}{  a numeric vector or matrix }
+}
+\details{
+  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_2}.
+  This is merely the entrywise norm with exponent 2.
+}
+\value{
+  A numeric value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
+  Hopkins University Press.
+
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{entrywise.norm}}
+}
+\examples{
+A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
+print( hilbert.schmidt.norm( A ) )
+}
+\keyword{ math }
diff --git a/man/inf.norm.Rd b/man/inf.norm.Rd
old mode 100644
new mode 100755
index f84eeec..002561b
--- a/man/inf.norm.Rd
+++ b/man/inf.norm.Rd
@@ -1,39 +1,39 @@
-\name{inf.norm}
-\alias{inf.norm}
-\title{ Compute the infinitity norm of a matrix }
-\description{
-  This function returns the \eqn{\left\| {\mathbf{x}} \right\|_\infty } norm of the matrix \eqn{{\mathbf{x}}}.
-}
-\usage{
-inf.norm(x)
-}
-\arguments{
-  \item{x}{  a numeric vector or matrix }
-}
-\details{
-  Let \eqn{{\bf{x}}} be an \eqn{m \times n} numeric matrix.
-  The formula used to compute the norm is 
-  \eqn{\left\| {\bf{x}} \right\|_\infty   = \mathop {\max }\limits_{1 \le i \le m} \sum\limits_{j = 1}^n {\left| {x_{i,j} } \right|} }.
-  This is merely the maximum absolute row sum of the \eqn{m \times n} maxtris.
-}
-\value{
-  A numeric value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
-  Hopkins University Press.
-
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{one.norm}}
-}
-\examples{
-A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
-print( inf.norm( A ) )
-}
-\keyword{ math }
+\name{inf.norm}
+\alias{inf.norm}
+\title{ Compute the infinitity norm of a matrix }
+\description{
+  This function returns the \eqn{\left\| {\mathbf{x}} \right\|_\infty } norm of the matrix \eqn{{\mathbf{x}}}.
+}
+\usage{
+inf.norm(x)
+}
+\arguments{
+  \item{x}{  a numeric vector or matrix }
+}
+\details{
+  Let \eqn{{\bf{x}}} be an \eqn{m \times n} numeric matrix.
+  The formula used to compute the norm is 
+  \eqn{\left\| {\bf{x}} \right\|_\infty   = \mathop {\max }\limits_{1 \le i \le m} \sum\limits_{j = 1}^n {\left| {x_{i,j} } \right|} }.
+  This is merely the maximum absolute row sum of the \eqn{m \times n} maxtris.
+}
+\value{
+  A numeric value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
+  Hopkins University Press.
+
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{one.norm}}
+}
+\examples{
+A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
+print( inf.norm( A ) )
+}
+\keyword{ math }
diff --git a/man/is.diagonal.matrix.Rd b/man/is.diagonal.matrix.Rd
old mode 100644
new mode 100755
index 499f7bb..c0251f0
--- a/man/is.diagonal.matrix.Rd
+++ b/man/is.diagonal.matrix.Rd
@@ -1,35 +1,35 @@
-\name{is.diagonal.matrix}
-\alias{is.diagonal.matrix}
-\title{ Test for diagonal square matrix }
-\description{
-  This function returns \code{TRUE} if the given matrix argument x
-  is a square numeric matrix and that the off-diagonal elements are close
-  to zero in absolute value to within the given tolerance level. Otherwise,
-  a \code{FALSE} value is returned.
-}
-\usage{
-is.diagonal.matrix(x, tol = 1e-08)
-}
-\arguments{
-  \item{x}{ a numeric square matrix }
-  \item{tol}{ a numeric tolerance level usually left out }
-}
-\value{
-  A TRUE or FALSE value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- diag( 1, 3 )
-is.diagonal.matrix( A )
-B <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
-is.diagonal.matrix( B )
-C <- matrix( c( 1, 0, 0, 0 ), nrow=2, byrow=TRUE )
-is.diagonal.matrix( C )
-}
-\keyword{ math }
+\name{is.diagonal.matrix}
+\alias{is.diagonal.matrix}
+\title{ Test for diagonal square matrix }
+\description{
+  This function returns \code{TRUE} if the given matrix argument x
+  is a square numeric matrix and that the off-diagonal elements are close
+  to zero in absolute value to within the given tolerance level. Otherwise,
+  a \code{FALSE} value is returned.
+}
+\usage{
+is.diagonal.matrix(x, tol = 1e-08)
+}
+\arguments{
+  \item{x}{ a numeric square matrix }
+  \item{tol}{ a numeric tolerance level usually left out }
+}
+\value{
+  A TRUE or FALSE value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- diag( 1, 3 )
+is.diagonal.matrix( A )
+B <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
+is.diagonal.matrix( B )
+C <- matrix( c( 1, 0, 0, 0 ), nrow=2, byrow=TRUE )
+is.diagonal.matrix( C )
+}
+\keyword{ math }
diff --git a/man/is.idempotent.matrix.Rd b/man/is.idempotent.matrix.Rd
old mode 100644
new mode 100755
index db605c8..2184478
--- a/man/is.idempotent.matrix.Rd
+++ b/man/is.idempotent.matrix.Rd
@@ -1,58 +1,58 @@
-\name{is.idempotent.matrix}
-\alias{is.idempotent.matrix}
-\title{ Test for idempotent square matrix }
-\description{
-  This function returns a \code{TRUE} value if the square matrix argument x
-  is idempotent, that is, the product of the matrix with itself is the matrix.
-  The equality test is performed to within the specified tolerance level.  If
-  the matrix is not idempotent, then a \code{FALSE} value is returned.
-}
-\usage{
-is.idempotent.matrix(x, tol = 1e-08)
-}
-\arguments{
-  \item{x}{ a numeric square matrix }
-  \item{tol}{ a numeric tolerance level usually left out }
-}
-\details{
-  Idempotent matrices are used in econometric analysis.  Consider the problem of
-  estimating the regression parameters of a standard linear model 
-  \eqn{{\bf{y}} = {\bf{X}}\;{\bf{\beta }} + {\bf{e}}} using the method of least squares.
-  \eqn{{\bf{y}}} is an order \eqn{m} random vector of dependent variables. 
-  \eqn{{\bf{X}}} is an \eqn{m \times n} matrix whose columns are columns of
-  observations on one of the \eqn{ n - 1} independent variables.  The first column
-  contains \eqn{m} ones.  \eqn{{\bf{e}}} is an order \eqn{m} random vector of zero
-  mean residual values.  \eqn{{\bf{\beta }}} is the order \eqn{n} vector of regression
-  parameters.  The objective function that is minimized in the method of least squares is
-  \eqn{\left( {{\bf{y}} - {\bf{X}}\;{\bf{\beta }}} \right)^\prime  \left( {{\bf{y}} - {\bf{X}}\;{\bf{\beta }}} \right)}.
-  The solution to ths quadratic programming problem is
-  \eqn{{\bf{\hat \beta }} = \left[ {\left( {{\bf{X'}}\;{\bf{X}}} \right)^{ - 1} \;{\bf{X'}}} \right]\;{\bf{y}}}
-  The corresponding estimator for the residual vector is
-  \eqn{{\bf{\hat e}} = {\bf{y}} - {\bf{X}}\;{\bf{\hat \beta }} = \left[ {{\bf{I}} - {\bf{X}}\;\left( {{\bf{X'}}\;{\bf{X}}} \right)^{ - 1} {\bf{X'}}} \right]{\bf{y}} = {\bf{M}}\;{\bf{y}}}.
-  \eqn{{\bf{M}}} and \eqn{{{\bf{X}}\;\left( {{\bf{X'}}\;{\bf{X}}} \right)^{ - 1} {\bf{X'}}}} are idempotent.
-  Idempotency of \eqn{{\bf{M}}} enters into the estimation of the variance of the estimator.
-}
-\value{
-  A TRUE or FALSE value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Chang, A. C., (1984). \emph{Fundamental Methods of Mathematical Economics},
-  Third edition, McGraw-Hill.
-
-  Green, W. H. (2003). \emph{Econometric Analysis}, Fifth edition, Prentice-Hall.
-  
-  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- diag( 1, 3 )
-is.idempotent.matrix( A )
-B <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
-is.idempotent.matrix( B )
-C <- matrix( c( 1, 0, 0, 0 ), nrow=2, byrow=TRUE )
-is.idempotent.matrix( C )
-}
-\keyword{ math }
+\name{is.idempotent.matrix}
+\alias{is.idempotent.matrix}
+\title{ Test for idempotent square matrix }
+\description{
+  This function returns a \code{TRUE} value if the square matrix argument x
+  is idempotent, that is, the product of the matrix with itself is the matrix.
+  The equality test is performed to within the specified tolerance level.  If
+  the matrix is not idempotent, then a \code{FALSE} value is returned.
+}
+\usage{
+is.idempotent.matrix(x, tol = 1e-08)
+}
+\arguments{
+  \item{x}{ a numeric square matrix }
+  \item{tol}{ a numeric tolerance level usually left out }
+}
+\details{
+  Idempotent matrices are used in econometric analysis.  Consider the problem of
+  estimating the regression parameters of a standard linear model 
+  \eqn{{\bf{y}} = {\bf{X}}\;{\bf{\beta }} + {\bf{e}}} using the method of least squares.
+  \eqn{{\bf{y}}} is an order \eqn{m} random vector of dependent variables. 
+  \eqn{{\bf{X}}} is an \eqn{m \times n} matrix whose columns are columns of
+  observations on one of the \eqn{ n - 1} independent variables.  The first column
+  contains \eqn{m} ones.  \eqn{{\bf{e}}} is an order \eqn{m} random vector of zero
+  mean residual values.  \eqn{{\bf{\beta }}} is the order \eqn{n} vector of regression
+  parameters.  The objective function that is minimized in the method of least squares is
+  \eqn{\left( {{\bf{y}} - {\bf{X}}\;{\bf{\beta }}} \right)^\prime  \left( {{\bf{y}} - {\bf{X}}\;{\bf{\beta }}} \right)}.
+  The solution to ths quadratic programming problem is
+  \eqn{{\bf{\hat \beta }} = \left[ {\left( {{\bf{X'}}\;{\bf{X}}} \right)^{ - 1} \;{\bf{X'}}} \right]\;{\bf{y}}}
+  The corresponding estimator for the residual vector is
+  \eqn{{\bf{\hat e}} = {\bf{y}} - {\bf{X}}\;{\bf{\hat \beta }} = \left[ {{\bf{I}} - {\bf{X}}\;\left( {{\bf{X'}}\;{\bf{X}}} \right)^{ - 1} {\bf{X'}}} \right]{\bf{y}} = {\bf{M}}\;{\bf{y}}}.
+  \eqn{{\bf{M}}} and \eqn{{{\bf{X}}\;\left( {{\bf{X'}}\;{\bf{X}}} \right)^{ - 1} {\bf{X'}}}} are idempotent.
+  Idempotency of \eqn{{\bf{M}}} enters into the estimation of the variance of the estimator.
+}
+\value{
+  A TRUE or FALSE value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Chang, A. C., (1984). \emph{Fundamental Methods of Mathematical Economics},
+  Third edition, McGraw-Hill.
+
+  Green, W. H. (2003). \emph{Econometric Analysis}, Fifth edition, Prentice-Hall.
+  
+  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- diag( 1, 3 )
+is.idempotent.matrix( A )
+B <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
+is.idempotent.matrix( B )
+C <- matrix( c( 1, 0, 0, 0 ), nrow=2, byrow=TRUE )
+is.idempotent.matrix( C )
+}
+\keyword{ math }
diff --git a/man/is.indefinite.Rd b/man/is.indefinite.Rd
old mode 100644
new mode 100755
index f9ae067..26ea54c
--- a/man/is.indefinite.Rd
+++ b/man/is.indefinite.Rd
@@ -1,72 +1,72 @@
-\name{is.indefinite}
-\alias{is.indefinite}
-\title{ Test matrix for positive indefiniteness }
-\description{
-  This function returns TRUE if the argument, a square symmetric real matrix x, is indefinite.
-  That is, the matrix has both positive and negative eigenvalues.
-}
-\usage{
-is.indefinite(x, tol=1e-8)
-}
-\arguments{
-  \item{x}{ a matrix }
-  \item{tol}{ a numeric tolerance level }
-}
-\details{
-  For an indefinite matrix, the matrix should positive and negative eigenvalues. The R function \code{eigen}
-  is used to compute the eigenvalues. If any of the eigenvalues is absolute value is less than the
-  given tolerance, that eigenvalue is replaced with zero. If the matrix has both positive and
-  negative eigenvalues, it is declared to be indefinite.
-}
-\value{
-  TRUE or FALSE.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.positive.definite}}, 
-  \code{\link{is.positive.semi.definite}}, 
-  \code{\link{is.negative.definite}}, 
-  \code{\link{is.negative.semi.definite}}
-}
-\examples{
-###
-### identity matrix is always positive definite
-###
-I <- diag( 1, 3 )
-is.indefinite( I )
-###
-### positive definite matrix
-### eigenvalues are 3.4142136 2.0000000 0.585786
-###
-A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
-is.indefinite( A )
-###
-### positive semi-defnite matrix
-### eigenvalues are 4.732051 1.267949 8.881784e-16
-###
-B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
-is.indefinite( B )
-###
-### negative definite matrix
-### eigenvalues are -0.5857864 -2.0000000 -3.4142136
-###
-C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
-is.indefinite( C )
-###
-### negative semi-definite matrix
-### eigenvalues are 1.894210e-16 -1.267949 -4.732051
-###
-D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
-is.indefinite( D )
-###
-### indefinite matrix
-### eigenvalues are 3.828427  1.000000 -1.828427
-###
-E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
-is.indefinite( E )
-}
-\keyword{ math }
+\name{is.indefinite}
+\alias{is.indefinite}
+\title{ Test matrix for positive indefiniteness }
+\description{
+  This function returns TRUE if the argument, a square symmetric real matrix x, is indefinite.
+  That is, the matrix has both positive and negative eigenvalues.
+}
+\usage{
+is.indefinite(x, tol=1e-8)
+}
+\arguments{
+  \item{x}{ a matrix }
+  \item{tol}{ a numeric tolerance level }
+}
+\details{
+  For an indefinite matrix, the matrix should positive and negative eigenvalues. The R function \code{eigen}
+  is used to compute the eigenvalues. If any of the eigenvalues is absolute value is less than the
+  given tolerance, that eigenvalue is replaced with zero. If the matrix has both positive and
+  negative eigenvalues, it is declared to be indefinite.
+}
+\value{
+  TRUE or FALSE.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.positive.definite}}, 
+  \code{\link{is.positive.semi.definite}}, 
+  \code{\link{is.negative.definite}}, 
+  \code{\link{is.negative.semi.definite}}
+}
+\examples{
+###
+### identity matrix is always positive definite
+###
+I <- diag( 1, 3 )
+is.indefinite( I )
+###
+### positive definite matrix
+### eigenvalues are 3.4142136 2.0000000 0.585786
+###
+A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
+is.indefinite( A )
+###
+### positive semi-defnite matrix
+### eigenvalues are 4.732051 1.267949 8.881784e-16
+###
+B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
+is.indefinite( B )
+###
+### negative definite matrix
+### eigenvalues are -0.5857864 -2.0000000 -3.4142136
+###
+C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
+is.indefinite( C )
+###
+### negative semi-definite matrix
+### eigenvalues are 1.894210e-16 -1.267949 -4.732051
+###
+D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
+is.indefinite( D )
+###
+### indefinite matrix
+### eigenvalues are 3.828427  1.000000 -1.828427
+###
+E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
+is.indefinite( E )
+}
+\keyword{ math }
diff --git a/man/is.negative.definite.Rd b/man/is.negative.definite.Rd
old mode 100644
new mode 100755
index acfccfa..20c77b0
--- a/man/is.negative.definite.Rd
+++ b/man/is.negative.definite.Rd
@@ -1,70 +1,70 @@
-\name{is.negative.definite}
-\alias{is.negative.definite}
-\title{ Test matrix for negative definiteness }
-\description{
-  This function returns TRUE if the argument, a square symmetric real matrix x, is negative definite.  
-}
-\usage{
-is.negative.definite(x, tol=1e-8)
-}
-\arguments{
-  \item{x}{ a matrix }
-  \item{tol}{ a numeric tolerance level }
-}
-\details{
-  For a negative definite matrix, the eigenvalues should be negative. The R function \code{eigen}
-  is used to compute the eigenvalues. If any of the eigenvalues in absolute value is less than
-  the given tolerance, that eigenvalue is replaced with zero. If any of the eigenvalues is greater than or equal to zero,
-  then the matrix is not negative definite.   Otherwise, the matrix is declared to be negative definite.
-}
-\value{
-  TRUE or FALSE.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.positive.definite}}, 
-  \code{\link{is.positive.semi.definite}}, 
-  \code{\link{is.negative.semi.definite}}, 
-  \code{\link{is.indefinite}}
-}
-\examples{
-###
-### identity matrix is always positive definite
-I <- diag( 1, 3 )
-is.negative.definite( I )
-###
-### positive definite matrix
-### eigenvalues are 3.4142136 2.0000000 0.585786
-###
-A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
-is.negative.definite( A )
-###
-### positive semi-defnite matrix
-### eigenvalues are 4.732051 1.267949 8.881784e-16
-###
-B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
-is.negative.definite( B )
-###
-### negative definite matrix
-### eigenvalues are -0.5857864 -2.0000000 -3.4142136
-###
-C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
-is.negative.definite( C )
-###
-### negative semi-definite matrix
-### eigenvalues are 1.894210e-16 -1.267949 -4.732051
-###
-D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
-is.negative.definite( D )
-###
-### indefinite matrix
-### eigenvalues are 3.828427  1.000000 -1.828427
-###
-E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
-is.negative.definite( E )
-}
-\keyword{ math }
+\name{is.negative.definite}
+\alias{is.negative.definite}
+\title{ Test matrix for negative definiteness }
+\description{
+  This function returns TRUE if the argument, a square symmetric real matrix x, is negative definite.  
+}
+\usage{
+is.negative.definite(x, tol=1e-8)
+}
+\arguments{
+  \item{x}{ a matrix }
+  \item{tol}{ a numeric tolerance level }
+}
+\details{
+  For a negative definite matrix, the eigenvalues should be negative. The R function \code{eigen}
+  is used to compute the eigenvalues. If any of the eigenvalues in absolute value is less than
+  the given tolerance, that eigenvalue is replaced with zero. If any of the eigenvalues is greater than or equal to zero,
+  then the matrix is not negative definite.   Otherwise, the matrix is declared to be negative definite.
+}
+\value{
+  TRUE or FALSE.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.positive.definite}}, 
+  \code{\link{is.positive.semi.definite}}, 
+  \code{\link{is.negative.semi.definite}}, 
+  \code{\link{is.indefinite}}
+}
+\examples{
+###
+### identity matrix is always positive definite
+I <- diag( 1, 3 )
+is.negative.definite( I )
+###
+### positive definite matrix
+### eigenvalues are 3.4142136 2.0000000 0.585786
+###
+A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
+is.negative.definite( A )
+###
+### positive semi-defnite matrix
+### eigenvalues are 4.732051 1.267949 8.881784e-16
+###
+B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
+is.negative.definite( B )
+###
+### negative definite matrix
+### eigenvalues are -0.5857864 -2.0000000 -3.4142136
+###
+C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
+is.negative.definite( C )
+###
+### negative semi-definite matrix
+### eigenvalues are 1.894210e-16 -1.267949 -4.732051
+###
+D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
+is.negative.definite( D )
+###
+### indefinite matrix
+### eigenvalues are 3.828427  1.000000 -1.828427
+###
+E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
+is.negative.definite( E )
+}
+\keyword{ math }
diff --git a/man/is.negative.semi.definite.Rd b/man/is.negative.semi.definite.Rd
old mode 100644
new mode 100755
index caf6eda..7d114a8
--- a/man/is.negative.semi.definite.Rd
+++ b/man/is.negative.semi.definite.Rd
@@ -1,71 +1,71 @@
-\name{is.negative.semi.definite}
-\alias{is.negative.semi.definite}
-\title{ Test matrix for negative semi definiteness }
-\description{
-  This function returns TRUE if the argument, a square symmetric real matrix x, is negative semi-negative.  
-}
-\usage{
-is.negative.semi.definite(x, tol=1e-8)
-}
-\arguments{
-  \item{x}{ a matrix }
-  \item{tol}{ a numeric tolerance level }
-}
-\details{
-  For a negative semi-definite matrix, the eigenvalues should be non-positive. 
-  The R function \code{eigen} is used to compute the eigenvalues. 
-  If any of the eigenvalues in absolute value is less than the given tolerance, that eigenvalue
-  is replaced with zero.  Then, if any of the eigenvalues is greater than zero, the matrix
-  is not negative semi-definite.  Otherwise, the matrix is declared to be negative semi-definite.
-}
-\value{
-  TRUE or FALSE.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.positive.definite}}, 
-  \code{\link{is.positive.semi.definite}}, 
-  \code{\link{is.negative.definite}}, 
-  \code{\link{is.indefinite}}
-}
-\examples{
-###
-### identity matrix is always positive definite
-I <- diag( 1, 3 )
-is.negative.semi.definite( I )
-###
-### positive definite matrix
-### eigenvalues are 3.4142136 2.0000000 0.585786
-###
-A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
-is.negative.semi.definite( A )
-###
-### positive semi-defnite matrix
-### eigenvalues are 4.732051 1.267949 8.881784e-16
-###
-B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
-is.negative.semi.definite( B )
-###
-### negative definite matrix
-### eigenvalues are -0.5857864 -2.0000000 -3.4142136
-###
-C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
-is.negative.semi.definite( C )
-###
-### negative semi-definite matrix
-### eigenvalues are 1.894210e-16 -1.267949 -4.732051
-###
-D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
-is.negative.semi.definite( D )
-###
-### indefinite matrix
-### eigenvalues are 3.828427  1.000000 -1.828427
-###
-E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
-is.negative.semi.definite( E )
-}
-\keyword{ math }
+\name{is.negative.semi.definite}
+\alias{is.negative.semi.definite}
+\title{ Test matrix for negative semi definiteness }
+\description{
+  This function returns TRUE if the argument, a square symmetric real matrix x, is negative semi-negative.  
+}
+\usage{
+is.negative.semi.definite(x, tol=1e-8)
+}
+\arguments{
+  \item{x}{ a matrix }
+  \item{tol}{ a numeric tolerance level }
+}
+\details{
+  For a negative semi-definite matrix, the eigenvalues should be non-positive. 
+  The R function \code{eigen} is used to compute the eigenvalues. 
+  If any of the eigenvalues in absolute value is less than the given tolerance, that eigenvalue
+  is replaced with zero.  Then, if any of the eigenvalues is greater than zero, the matrix
+  is not negative semi-definite.  Otherwise, the matrix is declared to be negative semi-definite.
+}
+\value{
+  TRUE or FALSE.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.positive.definite}}, 
+  \code{\link{is.positive.semi.definite}}, 
+  \code{\link{is.negative.definite}}, 
+  \code{\link{is.indefinite}}
+}
+\examples{
+###
+### identity matrix is always positive definite
+I <- diag( 1, 3 )
+is.negative.semi.definite( I )
+###
+### positive definite matrix
+### eigenvalues are 3.4142136 2.0000000 0.585786
+###
+A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
+is.negative.semi.definite( A )
+###
+### positive semi-defnite matrix
+### eigenvalues are 4.732051 1.267949 8.881784e-16
+###
+B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
+is.negative.semi.definite( B )
+###
+### negative definite matrix
+### eigenvalues are -0.5857864 -2.0000000 -3.4142136
+###
+C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
+is.negative.semi.definite( C )
+###
+### negative semi-definite matrix
+### eigenvalues are 1.894210e-16 -1.267949 -4.732051
+###
+D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
+is.negative.semi.definite( D )
+###
+### indefinite matrix
+### eigenvalues are 3.828427  1.000000 -1.828427
+###
+E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
+is.negative.semi.definite( E )
+}
+\keyword{ math }
diff --git a/man/is.non.singular.matrix.Rd b/man/is.non.singular.matrix.Rd
old mode 100644
new mode 100755
index 9bd840b..28f4288
--- a/man/is.non.singular.matrix.Rd
+++ b/man/is.non.singular.matrix.Rd
@@ -1,40 +1,40 @@
-\name{is.non.singular.matrix}
-\alias{is.non.singular.matrix}
-\title{ Test if matrix is non-singular }
-\description{
-  This function returns \code{TRUE} is the matrix argument is non-singular
-  and \code{FALSE} otherwise.
-}
-\usage{
-is.non.singular.matrix(x, tol = 1e-08)
-}
-\arguments{
-  \item{x}{ a numeric square matrix }
-  \item{tol}{ a numeric tolerance level usually left out }
-}
-\details{
-  The determinant of the matrix \code{x} is first computed.
-  If the absolute value of the determinant is greater than or equal to the given
-  tolerance level, then a \code{TRUE} value is returned.
-  Otherwise, a \code{FALSE} value is returned.
-}
-\value{
-  TRUE or FALSE value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.singular.matrix}}
-}
-\examples{
-A <- diag( 1, 3 )
-is.non.singular.matrix( A )
-B <- matrix( c( 0, 0, 3, 4 ), nrow=2, byrow=TRUE )
-is.non.singular.matrix( B )
-}
-\keyword{ math }
+\name{is.non.singular.matrix}
+\alias{is.non.singular.matrix}
+\title{ Test if matrix is non-singular }
+\description{
+  This function returns \code{TRUE} is the matrix argument is non-singular
+  and \code{FALSE} otherwise.
+}
+\usage{
+is.non.singular.matrix(x, tol = 1e-08)
+}
+\arguments{
+  \item{x}{ a numeric square matrix }
+  \item{tol}{ a numeric tolerance level usually left out }
+}
+\details{
+  The determinant of the matrix \code{x} is first computed.
+  If the absolute value of the determinant is greater than or equal to the given
+  tolerance level, then a \code{TRUE} value is returned.
+  Otherwise, a \code{FALSE} value is returned.
+}
+\value{
+  TRUE or FALSE value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.singular.matrix}}
+}
+\examples{
+A <- diag( 1, 3 )
+is.non.singular.matrix( A )
+B <- matrix( c( 0, 0, 3, 4 ), nrow=2, byrow=TRUE )
+is.non.singular.matrix( B )
+}
+\keyword{ math }
diff --git a/man/is.positive.definite.Rd b/man/is.positive.definite.Rd
old mode 100644
new mode 100755
index 9bda4d4..89f75b5
--- a/man/is.positive.definite.Rd
+++ b/man/is.positive.definite.Rd
@@ -1,70 +1,70 @@
-\name{is.positive.definite}
-\alias{is.positive.definite}
-\title{ Test matrix for positive definiteness }
-\description{
-  This function returns TRUE if the argument, a square symmetric real matrix x, is positive definite.  
-}
-\usage{
-is.positive.definite(x, tol=1e-8)
-}
-\arguments{
-  \item{x}{ a matrix }
-  \item{tol}{ a numeric tolerance level }
-}
-\details{
-  For a positive definite matrix, the eigenvalues should be positive. The R function \code{eigen}
-  is used to compute the eigenvalues. If any of the eigenvalues in absolute value is less than the
-  given tolerance, that eigenvalue is replaced with zero. If any of the eigenvalues is less than or equal to zero,
-  then the matrix is not positive definite.  Otherwise, the matrix is declared to be positive definite.
-}
-\value{
-  TRUE or FALSE.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.positive.semi.definite}}, 
-  \code{\link{is.negative.definite}}, 
-  \code{\link{is.negative.semi.definite}}, 
-  \code{\link{is.indefinite}}
-}
-\examples{
-###
-### identity matrix is always positive definite
-I <- diag( 1, 3 )
-is.positive.definite( I )
-###
-### positive definite matrix
-### eigenvalues are 3.4142136 2.0000000 0.585786
-###
-A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
-is.positive.definite( A )
-###
-### positive semi-defnite matrix
-### eigenvalues are 4.732051 1.267949 8.881784e-16
-###
-B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
-is.positive.definite( B )
-###
-### negative definite matrix
-### eigenvalues are -0.5857864 -2.0000000 -3.4142136
-###
-C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
-is.positive.definite( C )
-###
-### negative semi-definite matrix
-### eigenvalues are 1.894210e-16 -1.267949 -4.732051
-###
-D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
-is.positive.definite( D )
-###
-### indefinite matrix
-### eigenvalues are 3.828427  1.000000 -1.828427
-###
-E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
-is.positive.definite( E )
-}
-\keyword{ math }
+\name{is.positive.definite}
+\alias{is.positive.definite}
+\title{ Test matrix for positive definiteness }
+\description{
+  This function returns TRUE if the argument, a square symmetric real matrix x, is positive definite.  
+}
+\usage{
+is.positive.definite(x, tol=1e-8)
+}
+\arguments{
+  \item{x}{ a matrix }
+  \item{tol}{ a numeric tolerance level }
+}
+\details{
+  For a positive definite matrix, the eigenvalues should be positive. The R function \code{eigen}
+  is used to compute the eigenvalues. If any of the eigenvalues in absolute value is less than the
+  given tolerance, that eigenvalue is replaced with zero. If any of the eigenvalues is less than or equal to zero,
+  then the matrix is not positive definite.  Otherwise, the matrix is declared to be positive definite.
+}
+\value{
+  TRUE or FALSE.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.positive.semi.definite}}, 
+  \code{\link{is.negative.definite}}, 
+  \code{\link{is.negative.semi.definite}}, 
+  \code{\link{is.indefinite}}
+}
+\examples{
+###
+### identity matrix is always positive definite
+I <- diag( 1, 3 )
+is.positive.definite( I )
+###
+### positive definite matrix
+### eigenvalues are 3.4142136 2.0000000 0.585786
+###
+A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
+is.positive.definite( A )
+###
+### positive semi-defnite matrix
+### eigenvalues are 4.732051 1.267949 8.881784e-16
+###
+B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
+is.positive.definite( B )
+###
+### negative definite matrix
+### eigenvalues are -0.5857864 -2.0000000 -3.4142136
+###
+C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
+is.positive.definite( C )
+###
+### negative semi-definite matrix
+### eigenvalues are 1.894210e-16 -1.267949 -4.732051
+###
+D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
+is.positive.definite( D )
+###
+### indefinite matrix
+### eigenvalues are 3.828427  1.000000 -1.828427
+###
+E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
+is.positive.definite( E )
+}
+\keyword{ math }
diff --git a/man/is.positive.semi.definite.Rd b/man/is.positive.semi.definite.Rd
old mode 100644
new mode 100755
index 1632ed3..865d7bb
--- a/man/is.positive.semi.definite.Rd
+++ b/man/is.positive.semi.definite.Rd
@@ -1,70 +1,70 @@
-\name{is.positive.semi.definite}
-\alias{is.positive.semi.definite}
-\title{ Test matrix for positive semi-definiteness }
-\description{
-  This function returns TRUE if the argument, a square symmetric real matrix x, is positive  semi-definite.  
-}
-\usage{
-is.positive.semi.definite(x, tol=1e-8)
-}
-\arguments{
-  \item{x}{ a matrix }
-  \item{tol}{ a numeric tolerance level }
-}
-\details{
-  For a positive semi-definite matrix, the eigenvalues should be non-negative. The R function \code{eigen}
-  is used to compute the eigenvalues. If any of the eigenvalues is less than zero,
-  then the matrix is not positive semi-definite.  Otherwise, the matrix is declared
-  to be positive semi-definite.
-}
-\value{
-  TRUE or FALSE.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.positive.definite}}, 
-  \code{\link{is.negative.definite}}, 
-  \code{\link{is.negative.semi.definite}}, 
-  \code{\link{is.indefinite}}
-}
-\examples{
-###
-### identity matrix is always positive definite
-I <- diag( 1, 3 )
-is.positive.semi.definite( I )
-###
-### positive definite matrix
-### eigenvalues are 3.4142136 2.0000000 0.585786
-###
-A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
-is.positive.semi.definite( A )
-###
-### positive semi-defnite matrix
-### eigenvalues are 4.732051 1.267949 8.881784e-16
-###
-B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
-is.positive.semi.definite( B )
-###
-### negative definite matrix
-### eigenvalues are -0.5857864 -2.0000000 -3.4142136
-###
-C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
-is.positive.semi.definite( C )
-###
-### negative semi-definite matrix
-### eigenvalues are 1.894210e-16 -1.267949 -4.732051
-###
-D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
-is.positive.semi.definite( D )
-###
-### indefinite matrix
-### eigenvalues are 3.828427  1.000000 -1.828427
-###
-E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
-is.positive.semi.definite( E )
-}
-\keyword{ math }
+\name{is.positive.semi.definite}
+\alias{is.positive.semi.definite}
+\title{ Test matrix for positive semi-definiteness }
+\description{
+  This function returns TRUE if the argument, a square symmetric real matrix x, is positive  semi-definite.  
+}
+\usage{
+is.positive.semi.definite(x, tol=1e-8)
+}
+\arguments{
+  \item{x}{ a matrix }
+  \item{tol}{ a numeric tolerance level }
+}
+\details{
+  For a positive semi-definite matrix, the eigenvalues should be non-negative. The R function \code{eigen}
+  is used to compute the eigenvalues. If any of the eigenvalues is less than zero,
+  then the matrix is not positive semi-definite.  Otherwise, the matrix is declared
+  to be positive semi-definite.
+}
+\value{
+  TRUE or FALSE.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.positive.definite}}, 
+  \code{\link{is.negative.definite}}, 
+  \code{\link{is.negative.semi.definite}}, 
+  \code{\link{is.indefinite}}
+}
+\examples{
+###
+### identity matrix is always positive definite
+I <- diag( 1, 3 )
+is.positive.semi.definite( I )
+###
+### positive definite matrix
+### eigenvalues are 3.4142136 2.0000000 0.585786
+###
+A <- matrix( c( 2, -1, 0, -1, 2, -1, 0, -1, 2 ), nrow=3, byrow=TRUE )
+is.positive.semi.definite( A )
+###
+### positive semi-defnite matrix
+### eigenvalues are 4.732051 1.267949 8.881784e-16
+###
+B <- matrix( c( 2, -1, 2, -1, 2, -1, 2, -1, 2 ), nrow=3, byrow=TRUE )
+is.positive.semi.definite( B )
+###
+### negative definite matrix
+### eigenvalues are -0.5857864 -2.0000000 -3.4142136
+###
+C <- matrix( c( -2, 1, 0, 1, -2, 1, 0, 1, -2 ), nrow=3, byrow=TRUE )
+is.positive.semi.definite( C )
+###
+### negative semi-definite matrix
+### eigenvalues are 1.894210e-16 -1.267949 -4.732051
+###
+D <- matrix( c( -2, 1, -2, 1, -2, 1, -2, 1, -2 ), nrow=3, byrow=TRUE )
+is.positive.semi.definite( D )
+###
+### indefinite matrix
+### eigenvalues are 3.828427  1.000000 -1.828427
+###
+E <- matrix( c( 1, 2, 0, 2, 1, 2, 0, 2, 1 ), nrow=3, byrow=TRUE )
+is.positive.semi.definite( E )
+}
+\keyword{ math }
diff --git a/man/is.singular.matrix.Rd b/man/is.singular.matrix.Rd
old mode 100644
new mode 100755
index d41e401..28a6b63
--- a/man/is.singular.matrix.Rd
+++ b/man/is.singular.matrix.Rd
@@ -1,40 +1,40 @@
-\name{is.singular.matrix}
-\alias{is.singular.matrix}
-\title{  Test for singular square matrix }
-\description{
-  This function returns \code{TRUE} is the matrix argument is singular
-  and \code{FALSE} otherwise.
-}
-\usage{
-is.singular.matrix(x, tol = 1e-08)
-}
-\arguments{
-  \item{x}{ a numeric square matrix }
-  \item{tol}{ a numeric tolerance level usually left out }
-}
-\details{
-  The determinant of the matrix \code{x} is first computed.
-  If the absolute value of the determinant is less than the given
-  tolerance level, then a \code{TRUE} value is returned.
-  Otherwise, a \code{FALSE} value is returned.
-}
-\value{
-  A TRUE or FALSE value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.non.singular.matrix}}
-}
-\examples{
-A <- diag( 1, 3 )
-is.singular.matrix( A )
-B <- matrix( c( 0, 0, 3, 4 ), nrow=2, byrow=TRUE )
-is.singular.matrix( B )
-}
-\keyword{ math }
+\name{is.singular.matrix}
+\alias{is.singular.matrix}
+\title{  Test for singular square matrix }
+\description{
+  This function returns \code{TRUE} is the matrix argument is singular
+  and \code{FALSE} otherwise.
+}
+\usage{
+is.singular.matrix(x, tol = 1e-08)
+}
+\arguments{
+  \item{x}{ a numeric square matrix }
+  \item{tol}{ a numeric tolerance level usually left out }
+}
+\details{
+  The determinant of the matrix \code{x} is first computed.
+  If the absolute value of the determinant is less than the given
+  tolerance level, then a \code{TRUE} value is returned.
+  Otherwise, a \code{FALSE} value is returned.
+}
+\value{
+  A TRUE or FALSE value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.non.singular.matrix}}
+}
+\examples{
+A <- diag( 1, 3 )
+is.singular.matrix( A )
+B <- matrix( c( 0, 0, 3, 4 ), nrow=2, byrow=TRUE )
+is.singular.matrix( B )
+}
+\keyword{ math }
diff --git a/man/is.skew.symmetric.matrix.Rd b/man/is.skew.symmetric.matrix.Rd
old mode 100644
new mode 100755
index 3e9fa52..f38518a
--- a/man/is.skew.symmetric.matrix.Rd
+++ b/man/is.skew.symmetric.matrix.Rd
@@ -1,40 +1,40 @@
-\name{is.skew.symmetric.matrix}
-\alias{is.skew.symmetric.matrix}
-\title{ Test for a skew-symmetric matrix }
-\description{
-  This function returns \code{TRUE} if the matrix argument x is
-  a skew symmetric matrix, i.e., the transpose of the matrix is
-  the negative of the matrix.  Otherwise, \code{FALSE} is returned.
-}
-\usage{
-is.skew.symmetric.matrix(x, tol = 1e-08)
-}
-\arguments{
-  \item{x}{ a numeric square matrix }
-  \item{tol}{ a numeric tolerance level usually left out }
-}
-\details{
-  Let \eqn{{\bf{x}}} be an order \eqn{n} matrix.  If every element
-  of the matrix \eqn{{\bf{x}} + {\bf{x'}}} in absolute value is less
-  than the given tolerance, then the matrix argument is declared to be
-  skew symmetric.
-}
-\value{
-  A TRUE or FALSE value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- diag( 1, 3 )
-is.skew.symmetric.matrix( A )
-B <- matrix( c( 0, -2, -1, -2, 0, -4, 1, 4, 0 ), nrow=3, byrow=TRUE )
-is.skew.symmetric.matrix( B )
-C <- matrix( c( 0, 2, 1, 2, 0, 4, 1, 4, 0 ), nrow=3, byrow=TRUE )
-is.skew.symmetric.matrix( C )
-}
-\keyword{ math }
+\name{is.skew.symmetric.matrix}
+\alias{is.skew.symmetric.matrix}
+\title{ Test for a skew-symmetric matrix }
+\description{
+  This function returns \code{TRUE} if the matrix argument x is
+  a skew symmetric matrix, i.e., the transpose of the matrix is
+  the negative of the matrix.  Otherwise, \code{FALSE} is returned.
+}
+\usage{
+is.skew.symmetric.matrix(x, tol = 1e-08)
+}
+\arguments{
+  \item{x}{ a numeric square matrix }
+  \item{tol}{ a numeric tolerance level usually left out }
+}
+\details{
+  Let \eqn{{\bf{x}}} be an order \eqn{n} matrix.  If every element
+  of the matrix \eqn{{\bf{x}} + {\bf{x'}}} in absolute value is less
+  than the given tolerance, then the matrix argument is declared to be
+  skew symmetric.
+}
+\value{
+  A TRUE or FALSE value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Horn, R. A. and C. R. Johnson (1990). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- diag( 1, 3 )
+is.skew.symmetric.matrix( A )
+B <- matrix( c( 0, -2, -1, -2, 0, -4, 1, 4, 0 ), nrow=3, byrow=TRUE )
+is.skew.symmetric.matrix( B )
+C <- matrix( c( 0, 2, 1, 2, 0, 4, 1, 4, 0 ), nrow=3, byrow=TRUE )
+is.skew.symmetric.matrix( C )
+}
+\keyword{ math }
diff --git a/man/is.square.matrix.Rd b/man/is.square.matrix.Rd
old mode 100644
new mode 100755
index 447fce8..1502a2d
--- a/man/is.square.matrix.Rd
+++ b/man/is.square.matrix.Rd
@@ -1,27 +1,27 @@
-\name{is.square.matrix}
-\alias{is.square.matrix}
-\title{ Test for square matrix }
-\description{
-  The function returns TRUE if the argument is a square matrix and FALSE otherwise.
-}
-\usage{
-is.square.matrix(x)
-}
-\arguments{
-  \item{x}{ a matrix }
-}
-\value{
-  TRUE or FALSE
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
-is.square.matrix( A )
-B <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-is.square.matrix( B )
-}
-\keyword{ math }
+\name{is.square.matrix}
+\alias{is.square.matrix}
+\title{ Test for square matrix }
+\description{
+  The function returns TRUE if the argument is a square matrix and FALSE otherwise.
+}
+\usage{
+is.square.matrix(x)
+}
+\arguments{
+  \item{x}{ a matrix }
+}
+\value{
+  TRUE or FALSE
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
+is.square.matrix( A )
+B <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+is.square.matrix( B )
+}
+\keyword{ math }
diff --git a/man/is.symmetric.matrix.Rd b/man/is.symmetric.matrix.Rd
old mode 100644
new mode 100755
index 0c4e9f8..97feb2b
--- a/man/is.symmetric.matrix.Rd
+++ b/man/is.symmetric.matrix.Rd
@@ -1,34 +1,34 @@
-\name{is.symmetric.matrix}
-\alias{is.symmetric.matrix}
-\title{ Test for symmetric numeric matrix }
-\description{
-  This function returns TRUE if the argument is a numeric symmetric square matrix and FALSE otherwise.
-}
-\usage{
-is.symmetric.matrix(x)
-}
-\arguments{
-  \item{x}{ an R object }
-}
-\value{
-  TRUE or FALSE.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\note{ 
-  If the argument is not a numeric matrix, the function displays an error message and stops.
-  If the argument is not a square matrix, the function displays an error message and stops.
-}
-\seealso{
-  \code{\link{is.square.matrix}}
-}
-\examples{
-A <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
-is.symmetric.matrix( A )
-B <- matrix( c( 1, 2, 2, 1 ), nrow=2, byrow=TRUE )
-is.symmetric.matrix( B )
-}
-\keyword{ math }
+\name{is.symmetric.matrix}
+\alias{is.symmetric.matrix}
+\title{ Test for symmetric numeric matrix }
+\description{
+  This function returns TRUE if the argument is a numeric symmetric square matrix and FALSE otherwise.
+}
+\usage{
+is.symmetric.matrix(x)
+}
+\arguments{
+  \item{x}{ an R object }
+}
+\value{
+  TRUE or FALSE.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\note{ 
+  If the argument is not a numeric matrix, the function displays an error message and stops.
+  If the argument is not a square matrix, the function displays an error message and stops.
+}
+\seealso{
+  \code{\link{is.square.matrix}}
+}
+\examples{
+A <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
+is.symmetric.matrix( A )
+B <- matrix( c( 1, 2, 2, 1 ), nrow=2, byrow=TRUE )
+is.symmetric.matrix( B )
+}
+\keyword{ math }
diff --git a/man/lower.triangle.Rd b/man/lower.triangle.Rd
old mode 100644
new mode 100755
index a48e29c..524315b
--- a/man/lower.triangle.Rd
+++ b/man/lower.triangle.Rd
@@ -1,28 +1,28 @@
-\name{lower.triangle}
-\alias{lower.triangle}
-\title{ Lower triangle portion of a matrix }
-\description{
-  Returns the lower triangle including the diagonal of a square numeric matrix.
-}
-\usage{
-lower.triangle(x)
-}
-\arguments{
-  \item{x}{ a matrix }
-}
-\value{
-  A matrix.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\seealso{
-  \code{\link{is.square.matrix}}
-}
-\examples{
-B <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-lower.triangle( B )
-}
-\keyword{ math }
+\name{lower.triangle}
+\alias{lower.triangle}
+\title{ Lower triangle portion of a matrix }
+\description{
+  Returns the lower triangle including the diagonal of a square numeric matrix.
+}
+\usage{
+lower.triangle(x)
+}
+\arguments{
+  \item{x}{ a matrix }
+}
+\value{
+  A matrix.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\seealso{
+  \code{\link{is.square.matrix}}
+}
+\examples{
+B <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+lower.triangle( B )
+}
+\keyword{ math }
diff --git a/man/lu.decomposition.Rd b/man/lu.decomposition.Rd
old mode 100644
new mode 100755
index becdfde..1a03bd5
--- a/man/lu.decomposition.Rd
+++ b/man/lu.decomposition.Rd
@@ -1,52 +1,52 @@
-\name{lu.decomposition}
-\alias{lu.decomposition}
-\title{ LU Decomposition of Square Matrix }
-\description{
-  This function performs an LU decomposition of the given square matrix argument
-  the results are returned in a list of named components.  The Doolittle decomposition
-  method is used to obtain the lower and upper triangular matrices
-}
-\usage{
-lu.decomposition(x)
-}
-\arguments{
-  \item{x}{ a numeric square matrix }
-}
-\details{
-  The Doolittle decomposition without row exchanges is performed generating
-  the lower and upper triangular matrices separately rather than in one matrix.
-}
-\value{
-  A list with two named components.
-  \item{L }{The numeric lower triangular matrix}
-  \item{U }{The number upper triangular matrix}
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996). \emph{Matrix Computations}, Third Edition,
-  John Hopkins University Press
-  
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
-luA <- lu.decomposition( A )
-L <- luA$L
-U <- luA$U
-print( L )
-print( U )
-print( L \%*\% U )
-print( A )
-B <- matrix( c( 2, -1, -2, -4, 6, 3, -4, -2, 8 ), nrow=3, byrow=TRUE )
-luB <- lu.decomposition( B )
-L <- luB$L
-U <- luB$U
-print( L )
-print( U )
-print( L \%*\% U )
-print( B )
-}
-\keyword{ math }
+\name{lu.decomposition}
+\alias{lu.decomposition}
+\title{ LU Decomposition of Square Matrix }
+\description{
+  This function performs an LU decomposition of the given square matrix argument
+  the results are returned in a list of named components.  The Doolittle decomposition
+  method is used to obtain the lower and upper triangular matrices
+}
+\usage{
+lu.decomposition(x)
+}
+\arguments{
+  \item{x}{ a numeric square matrix }
+}
+\details{
+  The Doolittle decomposition without row exchanges is performed generating
+  the lower and upper triangular matrices separately rather than in one matrix.
+}
+\value{
+  A list with two named components.
+  \item{L }{The numeric lower triangular matrix}
+  \item{U }{The number upper triangular matrix}
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996). \emph{Matrix Computations}, Third Edition,
+  John Hopkins University Press
+  
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
+luA <- lu.decomposition( A )
+L <- luA$L
+U <- luA$U
+print( L )
+print( U )
+print( L \%*\% U )
+print( A )
+B <- matrix( c( 2, -1, -2, -4, 6, 3, -4, -2, 8 ), nrow=3, byrow=TRUE )
+luB <- lu.decomposition( B )
+L <- luB$L
+U <- luB$U
+print( L )
+print( U )
+print( L \%*\% U )
+print( B )
+}
+\keyword{ math }
diff --git a/man/matrix.inverse.Rd b/man/matrix.inverse.Rd
old mode 100644
new mode 100755
index a5b025f..4a5fa02
--- a/man/matrix.inverse.Rd
+++ b/man/matrix.inverse.Rd
@@ -1,29 +1,29 @@
-\name{matrix.inverse}
-\alias{matrix.inverse}
-\title{ Inverse of a square matrix }
-\description{
-  This function returns the inverse of a square matrix computed using the R function solve.
-}
-\usage{
-matrix.inverse(x)
-}
-\arguments{
-  \item{x}{ a square numeric matrix }
-}
-\value{
-  A matrix.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
-print( A )
-invA <- matrix.inverse( A )
-print( invA )
-print( A \%*\% invA )
-print( invA \%*\% A )
-}
-\keyword{ math }
+\name{matrix.inverse}
+\alias{matrix.inverse}
+\title{ Inverse of a square matrix }
+\description{
+  This function returns the inverse of a square matrix computed using the R function solve.
+}
+\usage{
+matrix.inverse(x)
+}
+\arguments{
+  \item{x}{ a square numeric matrix }
+}
+\value{
+  A matrix.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
+print( A )
+invA <- matrix.inverse( A )
+print( invA )
+print( A \%*\% invA )
+print( invA \%*\% A )
+}
+\keyword{ math }
diff --git a/man/matrix.power.Rd b/man/matrix.power.Rd
old mode 100644
new mode 100755
index b83699c..7daa761
--- a/man/matrix.power.Rd
+++ b/man/matrix.power.Rd
@@ -1,37 +1,37 @@
-\name{matrix.power}
-\alias{matrix.power}
-\title{ Matrix Raised to a Power }
-\description{
-  This function computes the k-th power of order n square matrix x
-  If k is zero, the order n identity matrix is returned.  argument k
-  must be an integer.
-}
-\usage{
-matrix.power(x, k)
-}
-\arguments{
-  \item{x}{ a numeric square matrix }
-  \item{k}{ a numeric exponent }
-}
-\details{
-  The matrix power is computed by successive matrix multiplications.  If the
-  exponent is zero, the order n identity matrix is returned.  If the exponent
-  is negative, the inverse of the matrix is raised to the given power.
-}
-\value{
-  An order \eqn{n} matrix.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
-matrix.power( A, -2 )
-matrix.power( A, -1 )
-matrix.power( A, 0 )
-matrix.power( A, 1 )
-matrix.power( A, 2 )
-}
-\keyword{ math }
+\name{matrix.power}
+\alias{matrix.power}
+\title{ Matrix Raised to a Power }
+\description{
+  This function computes the k-th power of order n square matrix x
+  If k is zero, the order n identity matrix is returned.  argument k
+  must be an integer.
+}
+\usage{
+matrix.power(x, k)
+}
+\arguments{
+  \item{x}{ a numeric square matrix }
+  \item{k}{ a numeric exponent }
+}
+\details{
+  The matrix power is computed by successive matrix multiplications.  If the
+  exponent is zero, the order n identity matrix is returned.  If the exponent
+  is negative, the inverse of the matrix is raised to the given power.
+}
+\value{
+  An order \eqn{n} matrix.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
+matrix.power( A, -2 )
+matrix.power( A, -1 )
+matrix.power( A, 0 )
+matrix.power( A, 1 )
+matrix.power( A, 2 )
+}
+\keyword{ math }
diff --git a/man/matrix.rank.Rd b/man/matrix.rank.Rd
old mode 100644
new mode 100755
index ee1505f..687d64e
--- a/man/matrix.rank.Rd
+++ b/man/matrix.rank.Rd
@@ -1,38 +1,38 @@
-\name{matrix.rank}
-\alias{matrix.rank}
-\title{ Rank of a square matrix }
-\description{
-  This function returns the rank of a square numeric matrix based on the selected method.
-}
-\usage{
-matrix.rank(x, method = c("qr", "chol"))
-}
-\arguments{
-  \item{x}{ a matrix }
-  \item{method}{ a character string that specifies the method to be used }
-}
-\details{
-  If the user specifies "qr" as the method, then the QR decomposition function is used to obtain the rank.
-  If the user specifies "chol" as the method, the rank is obtained from the attributes of the value returned.
-}
-\value{
-  An integer.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument is not a square numeric matrix, then the function presents an error message and stops.
-}
-\seealso{
-  \code{\link{is.square.matrix}}
-}  
-\examples{
-A <- diag( seq( 1, 4, 1 ) )
-matrix.rank( A )
-B <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-matrix.rank( B )
-}
-\keyword{ math }
+\name{matrix.rank}
+\alias{matrix.rank}
+\title{ Rank of a square matrix }
+\description{
+  This function returns the rank of a square numeric matrix based on the selected method.
+}
+\usage{
+matrix.rank(x, method = c("qr", "chol"))
+}
+\arguments{
+  \item{x}{ a matrix }
+  \item{method}{ a character string that specifies the method to be used }
+}
+\details{
+  If the user specifies "qr" as the method, then the QR decomposition function is used to obtain the rank.
+  If the user specifies "chol" as the method, the rank is obtained from the attributes of the value returned.
+}
+\value{
+  An integer.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument is not a square numeric matrix, then the function presents an error message and stops.
+}
+\seealso{
+  \code{\link{is.square.matrix}}
+}  
+\examples{
+A <- diag( seq( 1, 4, 1 ) )
+matrix.rank( A )
+B <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+matrix.rank( B )
+}
+\keyword{ math }
diff --git a/man/matrix.trace.Rd b/man/matrix.trace.Rd
old mode 100644
new mode 100755
index c997c95..fc0d720
--- a/man/matrix.trace.Rd
+++ b/man/matrix.trace.Rd
@@ -1,29 +1,29 @@
-\name{matrix.trace}
-\alias{matrix.trace}
-\title{ The trace of a matrix }
-\description{
-  This function returns the trace of a given square numeric matrix.
-}
-\usage{
-matrix.trace(x)
-}
-\arguments{
-  \item{x}{ a matrix }
-}
-\value{
-  A numeric value which is the sum of the values on the diagonal.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\note{
-  If the argument x is not numeric, the function presents and error message and terminates.
-  If the argument x is not a square matrix, the function presents an error message and terminates.
-}
-\examples{
-A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-matrix.trace( A )
-}
-\keyword{ math }
+\name{matrix.trace}
+\alias{matrix.trace}
+\title{ The trace of a matrix }
+\description{
+  This function returns the trace of a given square numeric matrix.
+}
+\usage{
+matrix.trace(x)
+}
+\arguments{
+  \item{x}{ a matrix }
+}
+\value{
+  A numeric value which is the sum of the values on the diagonal.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\note{
+  If the argument x is not numeric, the function presents and error message and terminates.
+  If the argument x is not a square matrix, the function presents an error message and terminates.
+}
+\examples{
+A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+matrix.trace( A )
+}
+\keyword{ math }
diff --git a/man/maximum.norm.Rd b/man/maximum.norm.Rd
old mode 100644
new mode 100755
index ca00b9c..bc45107
--- a/man/maximum.norm.Rd
+++ b/man/maximum.norm.Rd
@@ -1,38 +1,38 @@
-\name{maximum.norm}
-\alias{maximum.norm}
-\title{ Maximum norm of  matrix }
-\description{
-  This function returns the max norm of a real matrix.
-}
-\usage{
-maximum.norm(x)
-}
-\arguments{
-  \item{x}{ a numeric matrix or vector }
-}
-\details{
-  Let \eqn{{\bf{x}}} be an \eqn{m \times n} real matrix. The max norm returned
-  is \eqn{\left\| {\bf{x}} \right\|_{\max }  = \mathop {\max }\limits_{i,j} \left| {x_{i,j} } \right|}. 
-}
-\value{
-  A numeric value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
-  Hopkins University Press.
-
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{inf.norm}},
-  \code{\link{one.norm}}
-}
-\examples{
-A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
-maximum.norm( A )
-}
-\keyword{ math }
+\name{maximum.norm}
+\alias{maximum.norm}
+\title{ Maximum norm of  matrix }
+\description{
+  This function returns the max norm of a real matrix.
+}
+\usage{
+maximum.norm(x)
+}
+\arguments{
+  \item{x}{ a numeric matrix or vector }
+}
+\details{
+  Let \eqn{{\bf{x}}} be an \eqn{m \times n} real matrix. The max norm returned
+  is \eqn{\left\| {\bf{x}} \right\|_{\max }  = \mathop {\max }\limits_{i,j} \left| {x_{i,j} } \right|}. 
+}
+\value{
+  A numeric value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
+  Hopkins University Press.
+
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{inf.norm}},
+  \code{\link{one.norm}}
+}
+\examples{
+A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
+maximum.norm( A )
+}
+\keyword{ math }
diff --git a/man/one.norm.Rd b/man/one.norm.Rd
old mode 100644
new mode 100755
index d17b65d..d9d1c49
--- a/man/one.norm.Rd
+++ b/man/one.norm.Rd
@@ -1,38 +1,38 @@
-\name{one.norm}
-\alias{one.norm}
-\title{ Compute the one norm of a matrix }
-\description{
-  This function returns the \eqn{\left\| {\bf{x}} \right\|_1 } norm of the matrix \eqn{{\mathbf{x}}}.
-}
-\usage{
-one.norm(x)
-}
-\arguments{
-  \item{x}{  a numeric vector or matrix }
-}
-\details{
-  Let \eqn{{\bf{x}}} be an \eqn{m \times n} matrix. 
-  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_1  = \mathop {\max }\limits_{1 \le j \le n} \sum\limits_{i = 1}^m {\left| {x_{i,j} } \right|} }.
-  This is merely the maximum absolute column sum of the \eqn{m \times n} maxtris.
-}
-\value{
-  A numeric value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
-  Hopkins University Press.
-
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{inf.norm}}
-}
-\examples{
-A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
-one.norm( A )
-}
-\keyword{ math }
+\name{one.norm}
+\alias{one.norm}
+\title{ Compute the one norm of a matrix }
+\description{
+  This function returns the \eqn{\left\| {\bf{x}} \right\|_1 } norm of the matrix \eqn{{\mathbf{x}}}.
+}
+\usage{
+one.norm(x)
+}
+\arguments{
+  \item{x}{  a numeric vector or matrix }
+}
+\details{
+  Let \eqn{{\bf{x}}} be an \eqn{m \times n} matrix. 
+  The formula used to compute the norm is \eqn{\left\| {\bf{x}} \right\|_1  = \mathop {\max }\limits_{1 \le j \le n} \sum\limits_{i = 1}^m {\left| {x_{i,j} } \right|} }.
+  This is merely the maximum absolute column sum of the \eqn{m \times n} maxtris.
+}
+\value{
+  A numeric value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
+  Hopkins University Press.
+
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{inf.norm}}
+}
+\examples{
+A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
+one.norm( A )
+}
+\keyword{ math }
diff --git a/man/pascal.matrix.Rd b/man/pascal.matrix.Rd
old mode 100644
new mode 100755
index 878a463..333fdb3
--- a/man/pascal.matrix.Rd
+++ b/man/pascal.matrix.Rd
@@ -1,43 +1,43 @@
-\name{pascal.matrix}
-\alias{pascal.matrix}
-\title{ Pascal matrix }
-\description{
-  This function returns an n by n Pascal matrix.
-}
-\usage{
-pascal.matrix(n)
-}
-\arguments{
-  \item{n}{ Order of the matrix }
-}
-\details{
-  In mathematics, particularly matrix theory and combinatorics, the Pascal matrix is a lower triangular matrix
-  with binomial coefficients in the rows.  It is easily obtained by performing an LU decomposition on 
-  the symmetric Pascal matrix of the same order and returning the lower triangular matrix.
-}  
-\value{
-  An order \eqn{n} matrix.
-}
-\references{
-  Aceto, L. and D. Trigiante, (2001). Matrices of Pascal and Other Greats, \emph{American
-  Mathematical Monthly}, March 2001, 232-245.
-
-  Call, G. S. and D. J. Velleman, (1993). Pascal's matrices, \emph{American Mathematical Monthly},
-  April 1993, 100, 372-376.
-  
-  Edelman, A. and G. Strang, (2004). Pascal Matrices, \emph{American Mathematical Monthly},
-  111(3), 361-385.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not a positive integer, the function presents an error message and stops.
-}
-\seealso{
-  \code{\link{lu.decomposition}},
-  \code{\link{symmetric.pascal.matrix}}
-}
-\examples{
-P <- pascal.matrix( 4 )
-print( P )
-}
-\keyword{ math }
+\name{pascal.matrix}
+\alias{pascal.matrix}
+\title{ Pascal matrix }
+\description{
+  This function returns an n by n Pascal matrix.
+}
+\usage{
+pascal.matrix(n)
+}
+\arguments{
+  \item{n}{ Order of the matrix }
+}
+\details{
+  In mathematics, particularly matrix theory and combinatorics, the Pascal matrix is a lower triangular matrix
+  with binomial coefficients in the rows.  It is easily obtained by performing an LU decomposition on 
+  the symmetric Pascal matrix of the same order and returning the lower triangular matrix.
+}  
+\value{
+  An order \eqn{n} matrix.
+}
+\references{
+  Aceto, L. and D. Trigiante, (2001). Matrices of Pascal and Other Greats, \emph{American
+  Mathematical Monthly}, March 2001, 232-245.
+
+  Call, G. S. and D. J. Velleman, (1993). Pascal's matrices, \emph{American Mathematical Monthly},
+  April 1993, 100, 372-376.
+  
+  Edelman, A. and G. Strang, (2004). Pascal Matrices, \emph{American Mathematical Monthly},
+  111(3), 361-385.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not a positive integer, the function presents an error message and stops.
+}
+\seealso{
+  \code{\link{lu.decomposition}},
+  \code{\link{symmetric.pascal.matrix}}
+}
+\examples{
+P <- pascal.matrix( 4 )
+print( P )
+}
+\keyword{ math }
diff --git a/man/s.Rd b/man/s.Rd
old mode 100644
new mode 100755
index 4e951b2..2721a5c
--- a/man/s.Rd
+++ b/man/s.Rd
@@ -1,35 +1,35 @@
-\name{\%s\%}
-\alias{\%s\%}
-\title{ Direct sum of two arrays }
-\description{
-  This function computes the direct sum of two arrays.  The arrays can be
-  numerical vectors or matrices.  The result ia the block diagonal matrix.
-}  
-\usage{
-x\%s\%y
-}
-\arguments{
-  \item{x}{ a numeric matrix or vector }
-  \item{y}{ a numeric matrix or vector }
-}
-\value{
-  A numeric matrix.
-}
-\details{
-  If either \eqn{\bf{x}} or y is a vector, it is converted to a matrix.  The result
-  is a block diagonal matrix \eqn{\left\lbrack {\begin{array}{cc}
-   {\bf{x}} & {\bf{0}}  \\
-   {\bf{0}} & {\bf{y}}  \\
-\end{array}} \right\rbrack}.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
-\examples{
-x <- matrix( seq( 1, 4 ) )
-y <- matrix( seq( 5, 8 ) )
-print( x \%s\% y )
-}
-\keyword{ math }
+\name{\%s\%}
+\alias{\%s\%}
+\title{ Direct sum of two arrays }
+\description{
+  This function computes the direct sum of two arrays.  The arrays can be
+  numerical vectors or matrices.  The result ia the block diagonal matrix.
+}  
+\usage{
+x\%s\%y
+}
+\arguments{
+  \item{x}{ a numeric matrix or vector }
+  \item{y}{ a numeric matrix or vector }
+}
+\value{
+  A numeric matrix.
+}
+\details{
+  If either \eqn{\bf{x}} or y is a vector, it is converted to a matrix.  The result
+  is a block diagonal matrix \eqn{\left[ {\begin{array}{*{20}c}
+   {\bf{x}} & {\bf{0}}  \\
+   {\bf{0}} & {\bf{y}}  \\
+\end{array}} \right]}.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu}, Kurt Hornik \email{Kurt.Hornik@wu-wien.ac.at} }
+\examples{
+x <- matrix( seq( 1, 4 ) )
+y <- matrix( seq( 5, 8 ) )
+print( x \%s\% y )
+}
+\keyword{ math }
diff --git a/man/set.submatrix.Rd b/man/set.submatrix.Rd
old mode 100644
new mode 100755
index defe364..aca08f7
--- a/man/set.submatrix.Rd
+++ b/man/set.submatrix.Rd
@@ -1,34 +1,34 @@
-\name{set.submatrix}
-\alias{set.submatrix}
-\title{ Store matrix inside another matrix }
-\description{
-  This function returns a matrix which is a copy of matrix x into which the contents of matrix y
-  have been inserted at the given row and column.
-}
-\usage{
-set.submatrix(x, y, row, col)
-}
-\arguments{
-  \item{x}{ a matrix }
-  \item{y}{ a matrix }
-  \item{row}{ an integer row number }
-  \item{col}{ an integer column number }
-}
-\value{
-  A matrix.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument x is not a numeric matrix, then the function presents an error message and stops.
-  If the argument y is not a numeric matrix, then the function presents an error message and stops.
-  If the argument row is not a positive integer, then the function presents an error message and stops.
-  If the argument col is not a positive integer, then the function presents an error message and stops.
-  If the target row range does not overlap with the row range of argument x, then the function presents an error message and stops.
-  If the target col range does not overlap with the col range of argument x, then the function presents an error message and stops.
-}
-\examples{
-x <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-y <- matrix( seq( 1, 4, 1 ), nrow=2, byrow=TRUE )
-z <- set.submatrix( x, y, 3, 3 )
-}
-\keyword{ math }
+\name{set.submatrix}
+\alias{set.submatrix}
+\title{ Store matrix inside another matrix }
+\description{
+  This function returns a matrix which is a copy of matrix x into which the contents of matrix y
+  have been inserted at the given row and column.
+}
+\usage{
+set.submatrix(x, y, row, col)
+}
+\arguments{
+  \item{x}{ a matrix }
+  \item{y}{ a matrix }
+  \item{row}{ an integer row number }
+  \item{col}{ an integer column number }
+}
+\value{
+  A matrix.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument x is not a numeric matrix, then the function presents an error message and stops.
+  If the argument y is not a numeric matrix, then the function presents an error message and stops.
+  If the argument row is not a positive integer, then the function presents an error message and stops.
+  If the argument col is not a positive integer, then the function presents an error message and stops.
+  If the target row range does not overlap with the row range of argument x, then the function presents an error message and stops.
+  If the target col range does not overlap with the col range of argument x, then the function presents an error message and stops.
+}
+\examples{
+x <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+y <- matrix( seq( 1, 4, 1 ), nrow=2, byrow=TRUE )
+z <- set.submatrix( x, y, 3, 3 )
+}
+\keyword{ math }
diff --git a/man/shift.down.Rd b/man/shift.down.Rd
old mode 100644
new mode 100755
index d1f2644..afec229
--- a/man/shift.down.Rd
+++ b/man/shift.down.Rd
@@ -1,29 +1,29 @@
-\name{shift.down}
-\alias{shift.down}
-\title{ Shift matrix m rows down }
-\description{
-  This function returns a matrix that has had its rows shifted downwards filling the above rows
-  with the given fill value.
-}
-\usage{
-shift.down(A, rows = 1, fill = 0)
-}
-\arguments{
-  \item{A}{ a matrix }
-  \item{rows}{ the number of rows to be shifted }
-  \item{fill}{ the fill value which as a default is zero }
-}
-\value{
-  A matrix.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument A is not a numeric matrix, then the function presents an error message and stops.
-  If the argument rows is not a positive integer, then the function presents an error message and stops.
-}
-\examples{
-A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-shift.down( A, 1 )
-shift.down( A, 3 )
-}
-\keyword{ math }
+\name{shift.down}
+\alias{shift.down}
+\title{ Shift matrix m rows down }
+\description{
+  This function returns a matrix that has had its rows shifted downwards filling the above rows
+  with the given fill value.
+}
+\usage{
+shift.down(A, rows = 1, fill = 0)
+}
+\arguments{
+  \item{A}{ a matrix }
+  \item{rows}{ the number of rows to be shifted }
+  \item{fill}{ the fill value which as a default is zero }
+}
+\value{
+  A matrix.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument A is not a numeric matrix, then the function presents an error message and stops.
+  If the argument rows is not a positive integer, then the function presents an error message and stops.
+}
+\examples{
+A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+shift.down( A, 1 )
+shift.down( A, 3 )
+}
+\keyword{ math }
diff --git a/man/shift.left.Rd b/man/shift.left.Rd
old mode 100644
new mode 100755
index 5ad925b..b9ee980
--- a/man/shift.left.Rd
+++ b/man/shift.left.Rd
@@ -1,29 +1,29 @@
-\name{shift.left}
-\alias{shift.left}
-\title{ Shift a matrix n columns to the left }
-\description{
-  This function returns a matrix that has been shifted n columns to the left
-  filling the subsqeuent columns with the given fill value
-}
-\usage{
-shift.left(A, cols = 1, fill = 0)
-}
-\arguments{
-  \item{A}{ a matrix }
-  \item{cols}{ integer number of columns to be shifted to the left }
-  \item{fill}{ the fill value which as as a default zero }
-}
-\value{
-  A matrix.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument A is not a numeric matrix, then the function presents an error message and stops.
-  If the argument cols is not a positive integer, then the function presents an error message and stops.
-}
-\examples{
-A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
-shift.left( A, 1 )
-shift.left( A, 2 )
-}
-\keyword{ math }
+\name{shift.left}
+\alias{shift.left}
+\title{ Shift a matrix n columns to the left }
+\description{
+  This function returns a matrix that has been shifted n columns to the left
+  filling the subsqeuent columns with the given fill value
+}
+\usage{
+shift.left(A, cols = 1, fill = 0)
+}
+\arguments{
+  \item{A}{ a matrix }
+  \item{cols}{ integer number of columns to be shifted to the left }
+  \item{fill}{ the fill value which as as a default zero }
+}
+\value{
+  A matrix.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument A is not a numeric matrix, then the function presents an error message and stops.
+  If the argument cols is not a positive integer, then the function presents an error message and stops.
+}
+\examples{
+A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
+shift.left( A, 1 )
+shift.left( A, 2 )
+}
+\keyword{ math }
diff --git a/man/shift.right.Rd b/man/shift.right.Rd
old mode 100644
new mode 100755
index 9b85f90..29f0468
--- a/man/shift.right.Rd
+++ b/man/shift.right.Rd
@@ -1,29 +1,29 @@
-\name{shift.right}
-\alias{shift.right}
-\title{Shift matrix n columns to the right }
-\description{
-  This function returns a matrix that has been shifted to the right n columns
-  filling the previous columns with the given fill value.
-}
-\usage{
-shift.right(A, cols = 1, fill = 0)
-}
-\arguments{
-  \item{A}{ a matrix }
-  \item{cols}{ integer number of columns to be shifted to the right }
-  \item{fill}{ the fill which as default value zero }
-}
-\value{
-  A matrix.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument A is not a numeric matrix, then the function presents an error message and stops.
-  If the argument rows is not a positive integer, then the function presents an error message and stops.
-}
-\examples{
-A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-shift.right( A, 1 )
-shift.right( A, 2 )
-}
-\keyword{ math }
+\name{shift.right}
+\alias{shift.right}
+\title{Shift matrix n columns to the right }
+\description{
+  This function returns a matrix that has been shifted to the right n columns
+  filling the previous columns with the given fill value.
+}
+\usage{
+shift.right(A, cols = 1, fill = 0)
+}
+\arguments{
+  \item{A}{ a matrix }
+  \item{cols}{ integer number of columns to be shifted to the right }
+  \item{fill}{ the fill which as default value zero }
+}
+\value{
+  A matrix.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument A is not a numeric matrix, then the function presents an error message and stops.
+  If the argument rows is not a positive integer, then the function presents an error message and stops.
+}
+\examples{
+A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+shift.right( A, 1 )
+shift.right( A, 2 )
+}
+\keyword{ math }
diff --git a/man/shift.up.Rd b/man/shift.up.Rd
old mode 100644
new mode 100755
index aa4ed73..0cdb972
--- a/man/shift.up.Rd
+++ b/man/shift.up.Rd
@@ -1,29 +1,29 @@
-\name{shift.up}
-\alias{shift.up}
-\title{ Shift matrix m rows up }
-\description{
-  This function returns a matrix where the argument as been shifted up the given number of rows filling
-  the bottom rows with the given fill value.
-}
-\usage{
-shift.up(A, rows = 1, fill = 0)
-}
-\arguments{
-  \item{A}{ a matrix }
-  \item{rows}{ integer number of rows}
-  \item{fill}{ fill value which as the default value of zero }
-}
-\value{
-  A matrix.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument A is not a numeric matrix, then the function presents an error message and stops.
-  If the argument rows is not a positive integer, then the function presents an error message and stops.
-}
-\examples{
-A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-shift.up( A, 1 )
-shift.up( A, 3 )
-}
-\keyword{ math }
+\name{shift.up}
+\alias{shift.up}
+\title{ Shift matrix m rows up }
+\description{
+  This function returns a matrix where the argument as been shifted up the given number of rows filling
+  the bottom rows with the given fill value.
+}
+\usage{
+shift.up(A, rows = 1, fill = 0)
+}
+\arguments{
+  \item{A}{ a matrix }
+  \item{rows}{ integer number of rows}
+  \item{fill}{ fill value which as the default value of zero }
+}
+\value{
+  A matrix.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument A is not a numeric matrix, then the function presents an error message and stops.
+  If the argument rows is not a positive integer, then the function presents an error message and stops.
+}
+\examples{
+A <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+shift.up( A, 1 )
+shift.up( A, 3 )
+}
+\keyword{ math }
diff --git a/man/spectral.norm.Rd b/man/spectral.norm.Rd
old mode 100644
new mode 100755
index cdb6dc4..1df7bcf
--- a/man/spectral.norm.Rd
+++ b/man/spectral.norm.Rd
@@ -1,48 +1,48 @@
-\name{spectral.norm}
-\alias{spectral.norm}
-\title{ Spectral norm of  matrix }
-\description{
-  This function returns the spectral norm of a real matrix.
-}
-\usage{
-spectral.norm(x)
-}
-\arguments{
-  \item{x}{ a numeric matrix or vector }
-}
-\details{
-  Let \eqn{{\bf{x}}} be an \eqn{m \times n} real matrix.  The
-  function computes the order \eqn{n} square matrixmatrix \eqn{{\bf{A}} = {\bf{x'}}\;{\bf{x}}}.
-  The R function \code{eigen} is applied to this matrix to obtain the vector
-  of eigenvalues \eqn{{\bf{\lambda }} = \left\lbrack {\begin{array}{cccc}
-   {\lambda _1 } & {\lambda _2 } &  \cdots  & {\lambda _n }  \\
-\end{array}} \right\rbrack}.  By construction the eigenvalues are in descending
-  order of value so that the largest eigenvalue is \eqn{\lambda _1}.  Then
-  the spectral norm is \eqn{\left\| {\bf{x}} \right\|_2  = \sqrt {\lambda _1 }}.
-  If \eqn{{\bf{x}}} is a vector, then  \eqn{{\bf{L}}_2  = \sqrt {\bf{A}}} is returned.
-}
-\value{
-  A numeric value.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-
-  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
-  Hopkins University Press.
-
-  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument x is not numeric, an error message is displayed and the function terminates.
-  If the argument is neither a matrix nor a vector, an error message is displayed and the 
-  function terminates.
-  If the product matrix \eqn{{\bf{x'}}\;{\bf{x}}} is negative definite, an error message
-  displayed and the function terminates.
-}
-\examples{
-x <- matrix( c( 2, 4, 2, 1, 3, 1, 5, 2, 1, 2, 3, 3 ), nrow=3, ncol=4, byrow=TRUE )
-spectral.norm( x )
-}
-\keyword{ math }
+\name{spectral.norm}
+\alias{spectral.norm}
+\title{ Spectral norm of  matrix }
+\description{
+  This function returns the spectral norm of a real matrix.
+}
+\usage{
+spectral.norm(x)
+}
+\arguments{
+  \item{x}{ a numeric matrix or vector }
+}
+\details{
+  Let \eqn{{\bf{x}}} be an \eqn{m \times n} real matrix.  The
+  function computes the order \eqn{n} square matrixmatrix \eqn{{\bf{A}} = {\bf{x'}}\;{\bf{x}}}.
+  The R function \code{eigen} is applied to this matrix to obtain the vector
+  of eigenvalues \eqn{{\bf{\lambda }} = \left[ {\begin{array}{*{20}c}
+   {\lambda _1 } & {\lambda _2 } &  \cdots  & {\lambda _n }  \\
+\end{array}} \right]}.  By construction the eigenvalues are in descending
+  order of value so that the largest eigenvalue is \eqn{\lambda _1}.  Then
+  the spectral norm is \eqn{\left\| {\bf{x}} \right\|_2  = \sqrt {\lambda _1 }}.
+  If \eqn{{\bf{x}}} is a vector, then  \eqn{{\bf{L}}_2  = \sqrt {\bf{A}}} is returned.
+}
+\value{
+  A numeric value.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+
+  Golub, G. H. and C. F. Van Loan (1996).  \emph{Matrix Computations}, Third Edition, The John
+  Hopkins University Press.
+
+  Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument x is not numeric, an error message is displayed and the function terminates.
+  If the argument is neither a matrix nor a vector, an error message is displayed and the 
+  function terminates.
+  If the product matrix \eqn{{\bf{x'}}\;{\bf{x}}} is negative definite, an error message
+  displayed and the function terminates.
+}
+\examples{
+x <- matrix( c( 2, 4, 2, 1, 3, 1, 5, 2, 1, 2, 3, 3 ), nrow=3, ncol=4, byrow=TRUE )
+spectral.norm( x )
+}
+\keyword{ math }
diff --git a/man/stirling.matrix.Rd b/man/stirling.matrix.Rd
old mode 100644
new mode 100755
index 82f2e47..2600c7f
--- a/man/stirling.matrix.Rd
+++ b/man/stirling.matrix.Rd
@@ -1,50 +1,50 @@
-\name{stirling.matrix}
-\alias{stirling.matrix}
-\title{ Stirling Matrix }
-\description{
-  This function constructs and returns a Stirling matrix which is
-  a lower triangular matrix containing the Stirling numbers of
-  the second kind.
-}
-\usage{
-stirling.matrix(n)
-}
-\arguments{
-  \item{n}{  A positive integer value }
-}
-\details{
-  The Stirling numbers of the second kind, \eqn{S_i^j}, are used
-  in combinatorics to compute the number of ways a set of \eqn{i} objects
-  can be partitioned into \eqn{j} non-empty subsets \eqn{j \le i}.  The numbers are also
-  denoted by 
-  \eqn{\left\{ {\begin{array}{c}i\\j\end{array}} \right\}}.  Stirling numbers of
-  the second kind can be computed recursively with the equation
-  \eqn{S_j^{i + 1} = S_{j - 1}^i + j\;S_j^i,\quad 1 \le i \le n - 1,\;1 \le j \le i}.
-  The initial conditions for the recursion are
-  \eqn{S_i^i = 1,\quad 0 \le i \le n} and
-  \eqn{S_j^0 = S_0^j = 0,\quad 0 \le j \le n}.  The resultant numbers are organized
-  in an order \eqn{n + 1} matrix
-  \eqn{\left\lbrack {\begin{array}{ccccc}
-{S_0^0}&0&0& \cdots &0\\
-0&{S_1^1}&0& \cdots &0\\
-0&{S_1^2}&{S_2^2}& \cdots &0\\
- \cdots & \cdots & \cdots & \cdots & \cdots \\
-0&{S_1^n}&{S_2^n}& \cdots &{S_n^n}
-\end{array}} \right\rbrack}.
-}
-\value{
-  An order \eqn{n + 1} lower triangular matrix.
-}
-\references{
-  Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats,
-  \emph{American Mathematical Monthly}, March 2001, 108(3), 232-245.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not a positive integer, the function presents an error message and stops.
-}
-\examples{
-S <- stirling.matrix( 10 )
-print( S )
-}
-\keyword{ math }
+\name{stirling.matrix}
+\alias{stirling.matrix}
+\title{ Stirling Matrix }
+\description{
+  This function constructs and returns a Stirling matrix which is
+  a lower triangular matrix containing the Stirling numbers of
+  the second kind.
+}
+\usage{
+stirling.matrix(n)
+}
+\arguments{
+  \item{n}{  A positive integer value }
+}
+\details{
+  The Stirling numbers of the second kind, \eqn{S_i^j}, are used
+  in combinatorics to compute the number of ways a set of \eqn{i} objects
+  can be partitioned into \eqn{j} non-empty subsets \eqn{j \le i}.  The numbers are also
+  denoted by 
+  \eqn{\left\{ {\begin{array}{*{20}{c}}i\\j\end{array}} \right\}}.  Stirling numbers of
+  the second kind can be computed recursively with the equation
+  \eqn{S_j^{i + 1} = S_{j - 1}^i + j\;S_j^i,\quad 1 \le i \le n - 1,\;1 \le j \le i}.
+  The initial conditions for the recursion are
+  \eqn{S_i^i = 1,\quad 0 \le i \le n} and
+  \eqn{S_j^0 = S_0^j = 0,\quad 0 \le j \le n}.  The resultant numbers are organized
+  in an order \eqn{n + 1} matrix
+  \eqn{\left[ {\begin{array}{*{20}{c}}
+{S_0^0}&0&0& \cdots &0\\
+0&{S_1^1}&0& \cdots &0\\
+0&{S_1^2}&{S_2^2}& \cdots &0\\
+ \cdots & \cdots & \cdots & \cdots & \cdots \\
+0&{S_1^n}&{S_2^n}& \cdots &{S_n^n}
+\end{array}} \right]}.
+}
+\value{
+  An order \eqn{n + 1} lower triangular matrix.
+}
+\references{
+  Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats,
+  \emph{American Mathematical Monthly}, March 2001, 108(3), 232-245.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not a positive integer, the function presents an error message and stops.
+}
+\examples{
+S <- stirling.matrix( 10 )
+print( S )
+}
+\keyword{ math }
diff --git a/man/svd.inverse.Rd b/man/svd.inverse.Rd
old mode 100644
new mode 100755
index 7e7bc06..55cc7ab
--- a/man/svd.inverse.Rd
+++ b/man/svd.inverse.Rd
@@ -1,36 +1,36 @@
-\name{svd.inverse}
-\alias{svd.inverse}
-\title{ SVD Inverse of a square matrix }
-\description{
-  This function returns the inverse of a matrix using singular value
-  decomposition.  If the matrix is a square matrix, this should be equivalent
-  to using the \code{solve} function.  If the matrix is not a square matrix,
-  then the result is the Moore-Penrose pseudo inverse.
-}
-\usage{
-svd.inverse(x)
-}
-\arguments{
-  \item{x}{ a numeric matrix }
-}
-\value{
-  A matrix.
-}
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
-invA <- svd.inverse( A )
-print( A )
-print( invA )
-print( A \%*\% invA )
-B <- matrix( c( -1, 2, 2 ), nrow=1, byrow=TRUE )
-invB <- svd.inverse( B )
-print( B )
-print( invB )
-print( B \%*\% invB )
-}
-\keyword{ math }
+\name{svd.inverse}
+\alias{svd.inverse}
+\title{ SVD Inverse of a square matrix }
+\description{
+  This function returns the inverse of a matrix using singular value
+  decomposition.  If the matrix is a square matrix, this should be equivalent
+  to using the \code{solve} function.  If the matrix is not a square matrix,
+  then the result is the Moore-Penrose pseudo inverse.
+}
+\usage{
+svd.inverse(x)
+}
+\arguments{
+  \item{x}{ a numeric matrix }
+}
+\value{
+  A matrix.
+}
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
+invA <- svd.inverse( A )
+print( A )
+print( invA )
+print( A \%*\% invA )
+B <- matrix( c( -1, 2, 2 ), nrow=1, byrow=TRUE )
+invB <- svd.inverse( B )
+print( B )
+print( invB )
+print( B \%*\% invB )
+}
+\keyword{ math }
diff --git a/man/symmetric.pascal.matrix.Rd b/man/symmetric.pascal.matrix.Rd
old mode 100644
new mode 100755
index 5fbbe1a..7f8846d
--- a/man/symmetric.pascal.matrix.Rd
+++ b/man/symmetric.pascal.matrix.Rd
@@ -1,40 +1,40 @@
-\name{symmetric.pascal.matrix}
-\alias{symmetric.pascal.matrix}
-\title{ Symmetric Pascal matrix }
-\description{
-  This function returns an n by n symmetric Pascal matrix.
-}
-\usage{
-symmetric.pascal.matrix(n)
-}
-\arguments{
-  \item{n}{ Order of the matrix }
-}
-\details{
-  In mathematics, particularly matrix theory and combinatorics, the symmetric Pascal matrix is a square matrix
-  from which you can derive binomial coefficients.  The matrix is an order \eqn{n} symmetric
-  matrix with typical element given by \eqn{{S_{i,j}} = {{n!} \mathord{\left/
- {\vphantom {{n!} {\left[ {r!\;\left( {n - r} \right)!} \right]}}} \right.
- } {\left[ {r!\;\left( {n - r} \right)!} \right]}}} where
-  \eqn{n = i + j - 2} and \eqn{r = i - 1}.  The binomial coefficients are elegantly recovered from the
-  symmetric Pascal matrix by performing an \eqn{LU} decomposition as \eqn{{\bf{S}} = {\bf{L}}\;{\bf{U}}}.
-}  
-\value{
-  An order \eqn{n} matrix.
-}
-\references{
-  Call, G. S. and D. J. Velleman, (1993). Pascal's matrices, \emph{American Mathematical Monthly},
-  April 1993, 100, 372-376.
-  
-  Edelman, A. and G. Strang, (2004). Pascal Matrices, \emph{American Mathematical Monthly},
-  111(3), 361-385.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not a positive integer, the function presents an error message and stops.
-}
-\examples{
-S <- symmetric.pascal.matrix( 4 )
-print( S )
-}
-\keyword{ math }
+\name{symmetric.pascal.matrix}
+\alias{symmetric.pascal.matrix}
+\title{ Symmetric Pascal matrix }
+\description{
+  This function returns an n by n symmetric Pascal matrix.
+}
+\usage{
+symmetric.pascal.matrix(n)
+}
+\arguments{
+  \item{n}{ Order of the matrix }
+}
+\details{
+  In mathematics, particularly matrix theory and combinatorics, the symmetric Pascal matrix is a square matrix
+  from which you can derive binomial coefficients.  The matrix is an order \eqn{n} symmetric
+  matrix with typical element given by \eqn{{S_{i,j}} = {{n!} \mathord{\left/
+ {\vphantom {{n!} {\left[ {r!\;\left( {n - r} \right)!} \right]}}} \right.
+ \kern-\nulldelimiterspace} {\left[ {r!\;\left( {n - r} \right)!} \right]}}} where
+  \eqn{n = i + j - 2} and \eqn{r = i - 1}.  The binomial coefficients are elegantly recovered from the
+  symmetric Pascal matrix by performing an \eqn{LU} decomposition as \eqn{{\bf{S}} = {\bf{L}}\;{\bf{U}}}.
+}  
+\value{
+  An order \eqn{n} matrix.
+}
+\references{
+  Call, G. S. and D. J. Velleman, (1993). Pascal's matrices, \emph{American Mathematical Monthly},
+  April 1993, 100, 372-376.
+  
+  Edelman, A. and G. Strang, (2004). Pascal Matrices, \emph{American Mathematical Monthly},
+  111(3), 361-385.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not a positive integer, the function presents an error message and stops.
+}
+\examples{
+S <- symmetric.pascal.matrix( 4 )
+print( S )
+}
+\keyword{ math }
diff --git a/man/toeplitz.matrix.Rd b/man/toeplitz.matrix.Rd
old mode 100644
new mode 100755
index 4692a34..eaed41c
--- a/man/toeplitz.matrix.Rd
+++ b/man/toeplitz.matrix.Rd
@@ -1,34 +1,34 @@
-\name{toeplitz.matrix}
-\alias{toeplitz.matrix}
-\title{ Toeplitz Matrix }
-\description{
-  This function constructs an order n Toeplitz matrix from the values in
-  the order 2 * n - 1 vector x.
-}
-\usage{
-toeplitz.matrix(n, x)
-}
-\arguments{
-  \item{n}{ a positive integer value for order of matrix greater than 1 }
-  \item{x}{ a vector of values used to construct the matrix }
-}
-\details{
-  The element \code{T[i,j]} in the Toeplitz matrix is \code{x[i-j+n]}.
-}
-\value{
-  An order n matrix.
-}
-\references{
-  Monahan, J. F. (2011). \emph{Numerical Methods of Statistics}, Cambridge
-  University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument n is not a positive integer, the function presents an error message and stops.
-  If the length of x is not equal to 2 * n - 1, the function presents an error message and stops.
-}
-\examples{
-T <- toeplitz.matrix( 4, seq( 1, 7 ) )
-print( T )
-}
-\keyword{ math }
+\name{toeplitz.matrix}
+\alias{toeplitz.matrix}
+\title{ Toeplitz Matrix }
+\description{
+  This function constructs an order n Toeplitz matrix from the values in
+  the order 2 * n - 1 vector x.
+}
+\usage{
+toeplitz.matrix(n, x)
+}
+\arguments{
+  \item{n}{ a positive integer value for order of matrix greater than 1 }
+  \item{x}{ a vector of values used to construct the matrix }
+}
+\details{
+  The element \code{T[i,j]} in the Toeplitz matrix is \code{x[i-j+n]}.
+}
+\value{
+  An order n matrix.
+}
+\references{
+  Monahan, J. F. (2011). \emph{Numerical Methods of Statistics}, Cambridge
+  University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument n is not a positive integer, the function presents an error message and stops.
+  If the length of x is not equal to 2 * n - 1, the function presents an error message and stops.
+}
+\examples{
+T <- toeplitz.matrix( 4, seq( 1, 7 ) )
+print( T )
+}
+\keyword{ math }
diff --git a/man/u.vectors.Rd b/man/u.vectors.Rd
old mode 100644
new mode 100755
index 525f1b9..c92d4ea
--- a/man/u.vectors.Rd
+++ b/man/u.vectors.Rd
@@ -1,40 +1,40 @@
-\name{u.vectors}
-\alias{u.vectors}
-\title{ u vectors of an identity matrix }
-\description{
-  This function constructs an order n * ( n + 1 ) / 2 identity matrix
-  and an order matrix u that that maps the ordered pair of indices
-  (i,j) i=j, ..., n; j=1, ..., n to a column in this identity matrix.
-}
-\usage{
-u.vectors(n)
-}
-\arguments{
-  \item{n}{ a positive integer value for the order of underlying matrices }
-}
-\details{
-  The function firsts constructs an identity matrix of order \eqn{\frac{1}{2}n\left( {n + 1} \right)}.
-  \eqn{{{{\bf{u}}_{i,j}}}} is the column vector in the order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity
-  matrix for column \eqn{k = \left( {j - 1} \right)n + i - \frac{1}{2}j\left( {j - 1} \right)}.
-}
-\value{
-  A list with two named components
-  \item{k }{order \eqn{n} square matrix that maps each ordered pair (i,j) to a column in the identity matrix}
-  \item{I }{order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity matrix}
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
-  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
-  
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\note{
-  If the argument is not an integer, the function displays an error message and stops.
-  If the argument is less than two, the function displays an error message and stops.
-}
-\examples{
-u <- u.vectors( 3 )
-}
-\keyword{ math }
+\name{u.vectors}
+\alias{u.vectors}
+\title{ u vectors of an identity matrix }
+\description{
+  This function constructs an order n * ( n + 1 ) / 2 identity matrix
+  and an order matrix u that that maps the ordered pair of indices
+  (i,j) i=j, ..., n; j=1, ..., n to a column in this identity matrix.
+}
+\usage{
+u.vectors(n)
+}
+\arguments{
+  \item{n}{ a positive integer value for the order of underlying matrices }
+}
+\details{
+  The function firsts constructs an identity matrix of order \eqn{\frac{1}{2}n\left( {n + 1} \right)}.
+  \eqn{{{{\bf{u}}_{i,j}}}} is the column vector in the order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity
+  matrix for column \eqn{k = \left( {j - 1} \right)n + i - \frac{1}{2}j\left( {j - 1} \right)}.
+}
+\value{
+  A list with two named components
+  \item{k }{order \eqn{n} square matrix that maps each ordered pair (i,j) to a column in the identity matrix}
+  \item{I }{order \eqn{\frac{1}{2}n\left( {n + 1} \right)} identity matrix}
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications,
+  \emph{SIAM Journal on Algebraic Discrete Methods}, 1(4), December 1980, 422-449.
+  
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\note{
+  If the argument is not an integer, the function displays an error message and stops.
+  If the argument is less than two, the function displays an error message and stops.
+}
+\examples{
+u <- u.vectors( 3 )
+}
+\keyword{ math }
diff --git a/man/upper.triangle.Rd b/man/upper.triangle.Rd
old mode 100644
new mode 100755
index 6b5b618..51b3a4e
--- a/man/upper.triangle.Rd
+++ b/man/upper.triangle.Rd
@@ -1,28 +1,28 @@
-\name{upper.triangle}
-\alias{upper.triangle}
-\title{ Upper triangle portion of a matrix }
-\description{
-  Returns the lower triangle including the diagonal of a square numeric matrix.
-}
-\usage{
-upper.triangle(x)
-}
-\arguments{
-  \item{x}{ a matrix }
-}
-\value{
-  A matrix.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\references{
-  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
-  Society for Industrial and Applied Mathematics.
-}
-\seealso{
-  \code{\link{is.square.matrix}}
-}
-\examples{
-A <- matrix( seq( 1, 9, 1 ), nrow=3, byrow=TRUE )
-upper.triangle( A )
-}
-\keyword{ math }
+\name{upper.triangle}
+\alias{upper.triangle}
+\title{ Upper triangle portion of a matrix }
+\description{
+  Returns the lower triangle including the diagonal of a square numeric matrix.
+}
+\usage{
+upper.triangle(x)
+}
+\arguments{
+  \item{x}{ a matrix }
+}
+\value{
+  A matrix.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\references{
+  Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
+  Society for Industrial and Applied Mathematics.
+}
+\seealso{
+  \code{\link{is.square.matrix}}
+}
+\examples{
+A <- matrix( seq( 1, 9, 1 ), nrow=3, byrow=TRUE )
+upper.triangle( A )
+}
+\keyword{ math }
diff --git a/man/vandermonde.matrix.Rd b/man/vandermonde.matrix.Rd
old mode 100644
new mode 100755
index 063c17e..d363309
--- a/man/vandermonde.matrix.Rd
+++ b/man/vandermonde.matrix.Rd
@@ -1,41 +1,40 @@
-\name{vandermonde.matrix}
-\alias{vandermonde.matrix}
-\title{ Vandermonde matrix }
-\description{
-  This function returns an m by n matrix of the powers of the alpha vector
-}
-\usage{
-vandermonde.matrix(alpha, n)
-}
-\arguments{
-  \item{alpha}{ A numerical vector of values }
-  \item{n}{ The column dimension of the Vandermonde matrix }
-}
-\details{
-  In linear algebra, a Vandermonde matrix is an \eqn{m \times n} matrix with terms
-  of a geometric progression of an \eqn{m \times 1} parameter vector \eqn{{\bf{\alpha }} = {\left\lbrack {\begin{array}{cccc}
-{{\alpha _1}}&{{\alpha _2}}& \cdots &{{\alpha _m}}
-\end{array}} \right\rbrack^\prime }}
-
-  such that \eqn{V\left( {\bf{\alpha }} \right) = \left\lbrack {\begin{array}{ccccc}
-1&{{\alpha _1}}&{\alpha _1^2}& \cdots &{\alpha _1^{n - 1}}\\
-1&{{\alpha _2}}&{\alpha _2^2}& \cdots &{\alpha _2^{n - 1}}\\
-1&{{\alpha _3}}&{\alpha _3^2}& \cdots &{\alpha _3^{n - 1}}\\
- \cdots & \cdots & \cdots & \cdots & \cdots \\
-1&{{\alpha _m}}&{\alpha _m^2}& \cdots &{\alpha _m^{n - 1}}
-\end{array}} \right\rbrack}.
-}
-\value{
-  A matrix.
-}
-\references{
-  Horn, R. A. and C. R. Johnson (1991). \emph{Topics in matrix analysis}, Cambridge
-  University Press.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-alpha <- c( .1, .2, .3, .4 )
-V <- vandermonde.matrix( alpha, 4 )
-print( V )
-}
-\keyword{ math }
+\name{vandermonde.matrix}
+\alias{vandermonde.matrix}
+\title{ Vandermonde matrix }
+\description{
+  This function returns an m by n matrix of the powers of the alpha vector
+}
+\usage{
+vandermonde.matrix(alpha, n)
+}
+\arguments{
+  \item{alpha}{ A numerical vector of values }
+  \item{n}{ The column dimension of the Vandermonde matrix }
+}
+\details{
+  In linear algebra, a Vandermonde matrix is an \eqn{m \times n} matrix with terms
+  of a geometric progression of an \eqn{m \times 1} parameter vector \eqn{{\bf{\alpha }} = {\left[ {\begin{array}{*{20}{c}}
+{{\alpha _1}}&{{\alpha _2}}& \cdots &{{\alpha _m}}
+\end{array}} \right]^\prime }} 
+  such that \eqn{V\left( {\bf{\alpha }} \right) = \left[ {\begin{array}{*{20}{c}}
+1&{{\alpha _1}}&{\alpha _1^2}& \cdots &{\alpha _1^{n - 1}}\\
+1&{{\alpha _2}}&{\alpha _2^2}& \cdots &{\alpha _2^{n - 1}}\\
+1&{{\alpha _3}}&{\alpha _3^2}& \cdots &{\alpha _3^{n - 1}}\\
+ \cdots & \cdots & \cdots & \cdots & \cdots \\
+1&{{\alpha _m}}&{\alpha _m^2}& \cdots &{\alpha _m^{n - 1}}
+\end{array}} \right]}.
+}
+\value{
+  A matrix.
+}
+\references{
+  Horn, R. A. and C. R. Johnson (1991). \emph{Topics in matrix analysis}, Cambridge
+  University Press.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+alpha <- c( .1, .2, .3, .4 )
+V <- vandermonde.matrix( alpha, 4 )
+print( V )
+}
+\keyword{ math }
diff --git a/man/vec.Rd b/man/vec.Rd
old mode 100644
new mode 100755
index 46405a4..5cfb734
--- a/man/vec.Rd
+++ b/man/vec.Rd
@@ -1,27 +1,27 @@
-\name{vec}
-\alias{vec}
-\title{ Vectorize a matrix }
-\description{
-  This function returns a column vector that is a stack of the columns of x, an m by n matrix.
-}
-\usage{
-vec(x)
-}
-\arguments{
-  \item{x}{ a matrix }
-}
-\value{
-  A matrix with \eqn{m\;n} rows and one column.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\examples{
-x <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-print( x )
-vecx <- vec( x )
-print( vecx )
-}
-\keyword{ math }
+\name{vec}
+\alias{vec}
+\title{ Vectorize a matrix }
+\description{
+  This function returns a column vector that is a stack of the columns of x, an m by n matrix.
+}
+\usage{
+vec(x)
+}
+\arguments{
+  \item{x}{ a matrix }
+}
+\value{
+  A matrix with \eqn{m\;n} rows and one column.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\examples{
+x <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+print( x )
+vecx <- vec( x )
+print( vecx )
+}
+\keyword{ math }
diff --git a/man/vech.Rd b/man/vech.Rd
old mode 100644
new mode 100755
index 85a2f9d..3986e8e
--- a/man/vech.Rd
+++ b/man/vech.Rd
@@ -1,31 +1,31 @@
-\name{vech}
-\alias{vech}
-\title{ Vectorize a matrix }
-\description{
-  This function returns a stack of the lower triangular matrix of a square matrix as a matrix with 1 column
-  and n * ( n + 1 ) / 2 rows
-}
-\usage{
-vech(x)
-}
-\arguments{
-  \item{x}{ a matrix }
-}
-\value{
-  A matrix with \eqn{\frac{1}{2}n\left( {n + 1} \right)} rows and one column.
-}
-\references{
-  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
-  Second Edition, John Wiley.
-}
-\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
-\seealso{
-  \code{\link{is.square.matrix}}
-}
-\examples{
-x <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
-print( x )
-y <- vech( x )
-print( y )
-}
-\keyword{ math }
+\name{vech}
+\alias{vech}
+\title{ Vectorize a matrix }
+\description{
+  This function returns a stack of the lower triangular matrix of a square matrix as a matrix with 1 column
+  and n * ( n + 1 ) / 2 rows
+}
+\usage{
+vech(x)
+}
+\arguments{
+  \item{x}{ a matrix }
+}
+\value{
+  A matrix with \eqn{\frac{1}{2}n\left( {n + 1} \right)} rows and one column.
+}
+\references{
+  Magnus, J. R. and H. Neudecker (1999) \emph{Matrix Differential Calculus with Applications in Statistics and Econometrics},
+  Second Edition, John Wiley.
+}
+\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
+\seealso{
+  \code{\link{is.square.matrix}}
+}
+\examples{
+x <- matrix( seq( 1, 16, 1 ), nrow=4, byrow=TRUE )
+print( x )
+y <- vech( x )
+print( y )
+}
+\keyword{ math }

Debdiff

File lists identical (after any substitutions)

Control files: lines which differ (wdiff format)

Depends: r-base-core (>= 4.2.1-2), 4.2.0-1~jan+unchanged1), r-api-4.0

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