Explicit eigenvalues and inverses of several Toeplitz matrices

ANZIAM J. 48 (2006), 73-97

Explicit eigenvalues and inverses of several Toeplitz matrices

Wen-Chyuan Yueh
Department of Refrigeration
Chin-Yi Institute of Technology
Taichung
Taiwan 411
R. O. China
yuehwc@chinyi.ncit.edu.tw

and

Sui Sun Cheng
Department of Mathematics
Tsing Hua University
Hsinchu
Taiwan 30043
R. O. China

Abstract

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.

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