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\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 }
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