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\name{matrixpower}
\alias{matrixpower}
\alias{matrixsqrt}
\alias{matrixinvsqrt}
\title{
Power of a Matrix
}
\description{
Evaluate a specified power of a matrix.
}
\usage{
matrixpower(x, power, complexOK = TRUE)
matrixsqrt(x, complexOK = TRUE)
matrixinvsqrt(x, complexOK = TRUE)
}
\arguments{
\item{x}{
A square matrix containing numeric or complex values.
}
\item{power}{
A numeric value giving the power (exponent) to which \code{x} should
be raised.
}
\item{complexOK}{
Logical value indicating whether the result is allowed to be complex.
}
}
\details{
These functions raise the matrix \code{x} to the desired power:
\code{matrixsqrt} takes the square root, \code{matrixinvsqrt} takes
the inverse square root, and \code{matrixpower} takes the specified
power of \code{x}.
Up to numerical error, \code{matrixpower(x, 2)} should be equivalent
to \code{x \%*\% x}, and \code{matrixpower(x, -1)} should be
equivalent to \code{solve(x)}, the inverse of \code{x}.
The square root \code{y <- matrixsqrt(x)} should satisfy
\code{y \%*\% y = x}. The inverse square root
\code{z <- matrixinvsqrt(x)} should satisfy \code{z \%*\% z = solve(x)}.
Computations are performed using the eigen decomposition
(\code{\link{eigen}}).
}
\value{
A matrix of the same size as \code{x} containing
numeric or complex values.
}
\author{
\adrian.
}
\seealso{
\code{\link[base]{eigen}}, \code{\link[base]{svd}}
}
\examples{
x <- matrix(c(10,2,2,1), 2, 2)
y <- matrixsqrt(x)
y
y \%*\% y
z <- matrixinvsqrt(x)
z \%*\% y
matrixpower(x, 0.1)
}
\keyword{algebra}
\keyword{array}
|
