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Help  Striped matrices
Posted:
Jun 13, 1996 1:43 PM


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 nonzero diagonals are separated by two zero diagonals. Generally, the nonzero 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



