\name{rcond}
\title{Estimate the Reciprocal Condition Number}
\usage{
rcond(x, \dots)
}
\alias{rcond}
\alias{rcond.default}
\alias{rcond.Matrix}
\description{
    Estimate the reciprocal of the condition number of a matrix.
}
\arguments{
    \item{x}{
	a matrix. No missing values or IEEE special values are allowed.
    }
    \item{...}{
	additional arguments, for example to specify the matrix norm for
	which the condition number is to be estimated.
    }
}
\value{
    An estimate of the reciprocal condition number of \code{x}.
}
\section{BACKGROUND}{
    The condition number of a matrix is the product of the matrix and
    the norm of its inverse (or pseudo-inverse if the matrix is not
    square).
    Since it can take on values between 1 and infinity, inclusive, it
    can be viewed as a measure of how close a matrix is to being rank
    deficient.
    It can also be viewed as a factor by which errors in solving linear
    systems with this matrix as coefficient matrix could be magnified.

    Condition numbers are usually estimated, since exact computation is
    costly in terms of floating-point operations.
    An (over) estimate of reciprocal condition number is given, since by
    doing so overflow is avoided.
    Matrices are well-conditioned if the reciprocal condition number is
    near 1 and ill-conditioned if it is near zero.
}
\references{
Golub, G., and Van Loan, C. F. (1989).
\emph{Matrix Computations,}
2nd edition, Johns Hopkins, Baltimore.
}
\examples{
x <- Matrix(rnorm(9), 3, 3)
rcond(x)
rcond(hilbert(9))  # should be about 9.1e-13
h9 <- hilbert(9)
class(h9) <- Matrix.class(h9)  # now Hermitian
rcond(h9) # slightly different answer - different algorithm
}
\keyword{array}
\keyword{algebra}