Date: Jun 13, 1996 1:43 PM
Author: Doug Cochran
Subject: Help - Striped matrices



I have been trying to find information about a particular class of
sparse matrix with essentially no success. The class consists of
symmetric (or Hermetian) NxN matrices which are zero except on the
main diagonal and on additional diagonals uniformly spaced above and
below the main diagonal; e.g.,

[ * 0 0 * 0 0 * 0 0 * 0 ]
[ 0 * 0 0 * 0 0 * 0 0 * ]
[ 0 0 * 0 0 * 0 0 * 0 0 ]
[ * 0 0 * 0 0 * 0 0 * 0 ]
[ 0 * 0 0 * 0 0 * 0 0 * ]
[ 0 0 * 0 0 * 0 0 * 0 0 ]
[ * 0 0 * 0 0 * 0 0 * 0 ]
[ 0 * 0 0 * 0 0 * 0 0 * ]
[ 0 0 * 0 0 * 0 0 * 0 0 ]
[ * 0 0 * 0 0 * 0 0 * 0 ]
[ 0 * 0 0 * 0 0 * 0 0 * ]

In this example, the non-zero diagonals are separated by two zero
diagonals. Generally, the non-zero diagonals may be separated by
an arbitrary but fixed k>1 zero diagonals.

At this point, I am interested in more or less any known results
about invertibility, spectral structure, and transformation into
forms that have been more thoroughly studied (e.g., banded
matrix form).

Please send me email (cochran@asu.edu) if you know of any results
or references. I will post a summary if it seems warranted.

Doug Cochran
Arizona State University
Tempe, AZ USA