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
  Taiwan 411
  R. O. China
Sui Sun Cheng
  Department of Mathematics
  Tsing Hua University
  Taiwan 30043
  R. O. China

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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