\name{subspace}
\alias{subspace}
\title{Finds the angle between two subspaces.}
\description{
Finds the angle between two subspaces specified by the columns of A and B.
}
\usage{
subspace(A,B)
}
\arguments{
\item{A}{An p by u1 matrix. p must be greater than or equal to u1.}
\item{B}{An p by u2 matrix. p must be greater than or equal to u2.}
}
\details{  The algorithm used here ensures that small angles are computed
   accurately, and it allows subspaces of different dimensions following
   the definition in [2]. The first issue is crucial.  The second issue is
   not so important; but since the definition from [2] coinsides with the
   standard definition when the dimensions are equal, there should be no
   confusion - and subspaces with different dimensions may arise in
   problems where the dimension is computed as the numerical rank of some
   inaccurate matrix.
}
\value{the angle between two subspaces specified by the columns of A and B
}

\references{
[1] A. Bjorck & G. Golub, Numerical methods for computing angles between linear subspaces, Math. Comp. 27 (1973), pp. 579-594.

[2] P.-A. Wedin, On angles between subspaces of a finite dimensional inner product space, in B. Kagstrom & A. Ruhe (Eds.), Matrix Pencils, Lecture Notes in Mathematics 973, Springer, 1983, pp. 263-285.
}