# singular matrix

Matthew Knepley knepley at gmail.com
Thu Apr 16 15:17:13 CDT 2009

```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