https://github.com/cran/pracma
Tip revision: e970b8e92676e0d1f2c84b116f0bad93b03b89c6 authored by Hans W. Borchers on 15 December 2019, 21:30:02 UTC
version 2.2.9
version 2.2.9
Tip revision: e970b8e
orth.Rd
\name{orth}
\alias{orth}
\title{
Range Space
}
\description{
Range space or image of a matrix.
}
\usage{
orth(M)
}
\arguments{
\item{M}{Numeric matrix; vectors will be considered as column vectors.}
}
\details{
\code{B=orth(A)} returns an orthonormal basis for the range of \code{A}.
The columns of \code{B} span the same space as the columns of \code{A},
and the columns of \code{B} are orthogonal to each other.
The number of columns of \code{B} is the rank of \code{A}.
}
\value{
Matrix of orthogonal columns, spanning the image of \code{M}.
}
\references{
Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM,
Philadelphia.
}
\seealso{
\code{\link{nullspace}}
}
\examples{
M <- matrix(1:12, 3, 4)
Rank(M) #=> 2
orth(M)
}
\keyword{ array }