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\alias{det}
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\alias{det}
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\alias{determinant}
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\alias{determinant}
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\alias{determinant.matrix}
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\alias{determinant.matrix}
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\usage{
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\usage{
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det(x, \dots)
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det(x, \dots)
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determinant(x, logarithm, \dots)
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determinant(x, logarithm = TRUE, \dots)
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}
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}
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\description{
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\description{
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  \code{det} calculates the determinant of a matrix. \code{determinant}
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  \code{det} calculates the determinant of a matrix. \code{determinant}
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  is a generic function that returns separately the modulus of the determinant,
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  is a generic function that returns separately the modulus of the determinant,
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  optionally on the logarithm scale, and the sign of the determinant.
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  optionally on the logarithm scale, and the sign of the determinant.
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  }
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  }
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\arguments{
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\arguments{
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  \item{x}{numeric matrix.}
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  \item{x}{numeric matrix.}
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  \item{logarithm}{logical; if \code{TRUE} return the logarithm of the
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  \item{logarithm}{logical; if \code{TRUE} (default) return the
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    modulus of the determinant.  Default is \code{TRUE}.}
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    logarithm of the modulus of the determinant.}
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  \item{\dots}{Optional arguments.  At present none are used.  Previous
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  \item{\dots}{Optional arguments.  At present none are used.  Previous
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    versions of \code{det} allowed an optional \code{method} argument.
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    versions of \code{det} allowed an optional \code{method} argument.
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    This argument will be ignored but will not produce an error.}
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    This argument will be ignored but will not produce an error.}
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}
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}
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\value{
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\value{
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  For \code{det}, the determinant of \code{x}.  For \code{determinant}, a
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  For \code{det}, the determinant of \code{x}.  For \code{determinant}, a
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  list with components
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  list with components
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  \item{modulus}{a numeric value. The modulus (absolute value) of the
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  \item{modulus}{a numeric value.  The modulus (absolute value) of the
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    determinant if \code{logarithm} is \code{FALSE}; otherwise the
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    determinant if \code{logarithm} is \code{FALSE}; otherwise the
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    logarithm of the modulus.}
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    logarithm of the modulus.}
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  \item{sign}{integer; either \eqn{+1} or \eqn{-1} according to whether
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  \item{sign}{integer; either \eqn{+1} or \eqn{-1} according to whether
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    the determinant is positive or negative.}
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    the determinant is positive or negative.}
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}
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}