singular matrix
Chetan Jhurani
chetan at ices.utexas.edu
Thu Apr 16 15:05:15 CDT 2009
> 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
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