On Thu, Apr 16, 2009 at 3:05 PM, Chetan Jhurani <chetan at ices.utexas.edu>wrote:
> > > 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. > The definition that makes the most sense (and generalizes far beyond matrices) is |ker(A)| > 0. Matt > > > 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 > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20090416/2cd4e8f3/attachment.htm>
