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\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 }
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