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Explicit eigenvalues and inverses of several Toeplitz matrices

Published online by Cambridge University Press:  17 February 2009

Wen-Chyuan Yueh  and
Sui Sun Cheng
Wen-Chyuan Yueh
Affiliation:
Department of Refrigeration, Chin-Yi Institute of Technology, Taichung, Taiwan 411, R. O., China; e-mail: yuehwc@chinyi.ncit.edu.tw
Sui Sun Cheng
Affiliation:
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R. O., China
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Abstract

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Based on the theory of difference equations, we derive necessary and sufficient conditions for the existence of eigenvalues and inverses of Toeplitz matrices with five different diagonals. In the course of derivations, we are also able to derive computational formulas for the eigenvalues, eigenvectors and inverses of these matrices. A number of explicit formulas are computed for illustration and verification.

Keywords

Toeplitz matrixeigenvalueeigenvectorinversedifference equationsequence.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 1 , July 2006 , pp. 73 - 97
Copyright
Copyright © Australian Mathematical Society 2006

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