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Re: Help  Striped matrices
Posted:
Jun 13, 1996 9:39 PM


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



