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Topic: Help - Striped matrices
Replies: 2   Last Post: Jun 13, 1996 9:39 PM

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Moo Kyung Chung

Posts: 4
Registered: 12/12/04
Re: Help - Striped matrices
Posted: Jun 13, 1996 9:39 PM
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In article <Dsy98s.MpB@ennews.eas.asu.edu>,
Doug Cochran <cochran@trcsun3.eas.asu.edu> wrote:
>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


check out circulant matrix. circulant matrix has a remarkable property.
fourier matrix can diagonalize ANY circulant matrix.









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