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