Subset selection for matrices (Q874986)

The authors consider the question of how to delete \(m - k\) rows from an \(m \times n\) real matrix \(X\) so that the resulting \(k \times n\) matrix \(A\) is as nonsingular as possible. They derive bounds for the singular values of \(A\) which decrease only algebraically with \(m\) and \(n\). Applications of these bounds are also given.