> From: Matthew Knepley > > On Thu, Apr 16, 2009 at 11:34 AM, Chetan Jhurani <chetan at ices.utexas.edu> > wrote: > > > Only a square matrix can be singular. > > No, a singular matrix has a kernel. A non-square matrix can be singular.
One can generalize the concept of singular for rank-deficient rectangular matrices, but almost all usual definitions of singular matrix use non-invertibility or determinant and thus restrict themselves to square matrices. For example, http://mathworld.wolfram.com/SingularMatrix.html. > > If rank(A) = n, see > > <http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#The_QR_method> > > QR will work for a matrix of rank < n. In this case, a null space basis fills > out U. Agreed. Chetan
