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\name{inf.norm}
\alias{inf.norm}
\title{ Compute the infinitity norm of a matrix }
\description{
This function returns the \eqn{\left\| {\mathbf{x}} \right\|_\infty } norm of the matrix \eqn{{\mathbf{x}}}.
}
\usage{
inf.norm(x)
}
\arguments{
\item{x}{ a numeric vector or matrix }
}
\details{
Let \eqn{{\bf{x}}} be an \eqn{m \times n} numeric matrix.
The formula used to compute the norm is
\eqn{\left\| {\bf{x}} \right\|_\infty = \mathop {\max }\limits_{1 \le i \le m} \sum\limits_{j = 1}^n {\left| {x_{i,j} } \right|} }.
This is merely the maximum absolute row sum of the \eqn{m \times n} maxtris.
}
\value{
A numeric value.
}
\references{
Bellman, R. (1987). \emph{Matrix Analysis}, Second edition, Classics in Applied Mathematics,
Society for Industrial and Applied Mathematics.
Golub, G. H. and C. F. Van Loan (1996). \emph{Matrix Computations}, Third Edition, The John
Hopkins University Press.
Horn, R. A. and C. R. Johnson (1985). \emph{Matrix Analysis}, Cambridge University Press.
}
\author{ Frederick Novomestky \email{fnovomes@poly.edu} }
\seealso{
\code{\link{one.norm}}
}
\examples{
A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
print( inf.norm( A ) )
}
\keyword{ math }
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