\name{is.pdm}
\alias{is.pdm}
\title{Checks if a matrix is positive definite.}
\description{

  This checks if a matrix is positive definite and hence a valid
  covariance or precision matrix.  Note that if the argument is not a
  square matrix, it returns \code{FALSE}, and it should not signal an
  error. 

}
\usage{
is.pdm(m, tol = sqrt(.Machine$double.eps))
}
\arguments{
  \item{m}{Matrix to be tested.}
  \item{tol}{Tolerance check for symmetry and zero eignevalues.}
}
\details{
  A matrix \code{m} is considered positive definite if it has the
  following properites.
  \enumerate{
    \item{It is a matrix.}
    \item{It is numeric (complex matrixes are not considered).}
    \item{No entries are \code{NA}.}
    \item{It is square.}
    \item{It is symmetric (\code{m} is equal to \code{t(m)} within the
      specified tolerance).}
    \item{All of the eigenvalues are at least as big as \code{tol}.}
  }

  Note that this function is designed to return \code{FALSE} if any of
  the values are true, including non-matrix arguments.

}
\value{
  A logical scalar indicating whether or not the argument is positive
  definite. 
}
\author{Russell Almond}
\seealso{
  The \code{\link{is.pd}()} method of \code{\link{TimelessNormalParam}}
  uses this method by default to determine if the scale matrix is
  positive definite.
}
\examples{
stopifnot(
  is.pdm(diag(1:3)),
  is.pdm(matrix(c(.7,.3,.3,.7),2,2)),
  !is.pdm(matrix(1,2,2)),
  !is.pdm(matrix(NA,2,2)),
  !is.pdm(matrix(c(1,0,0,.3,1,.4),3,2)),
  !is.pdm(1:10)
)
}
\keyword{ algebra }