Remarks on band matrices |
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Authors: | L Elsner R M Redheffer |
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Institution: | (1) Department of Mathematics, University of California, 90024 Los Angeles, California, USA;(2) Institut für Angewandte Mathematik der Universität Hamburg, Rothenbaumchaussee 67/69, 2000 Hamburg 13 |
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Abstract: | In this note we consider band- or tridiagonal-matrices of orderk whose elements above, on, and below the diagonal are denoted byb
i
,a
i,c
i
. In the periodic case, i.e.b
i+m
=b
i
etc., we derive fork=nm andk=nm–1 formulas for the characteristic polynomial and the eigenvectors under the assumption that
i=1 In the latter case it is shown that the characteristic polynomial is divisible by them–1-th minor, as was already observed byRósa. We also give estimations for the number of real roots and an application to Fibonacci numbers. |
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Keywords: | |
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