Explicit determinants, inverses and eigenvalues of four band Toeplitz matrices with perturbed rows

Maoyun Zhang,Xiaoyu Jiang,Zhaolin Jiang

doi:10.1515/spma-2019-0004

Abstract

Abstract In this paper, four-band Toeplitz matrices and four-band Hankel matrices of type I and type II with perturbed rows are introduced. Explicit determinants, inverses and eigenvalues for these matrices are derived by using a nice inverse formula of block bidiagonal Toeplitz matrices.

Highlights

Throughout this paper, we consider explicit determinants, inverses and eigenvalues for two classes of fourband Toeplitz and Hankel matrices with perturbed rows, respectively.An n × n matrix M =n×n is said to be a perturbed Toeplitz four-band matrix of type I if its entries are de ned as a i=j=, b i =, j = n, c i = n, j =,d i = j = n, di,j = sn−j i=, ≤j≤n−, −f≤ j − i ≤, ≤ i, j ≤ n −, f +(− )i− i−j=,≤ i, j ≤ n −, tn−j i = n, ≤ j ≤ n −, otherwise, Open Access. 4.0 License
Inverses and eigenvalues for these matrices are derived by using a nice inverse formula of block bidiagonal Toeplitz matrices
Remark The result of Theorem 3.1 is somewhat surprising as the determinant of M is independent of si, ti ( ≤ i ≤ n − )

Summary

Introduction

Throughout this paper, we consider explicit determinants, inverses and eigenvalues for two classes of fourband Toeplitz and Hankel matrices with perturbed rows, respectively.

JK SR

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Corollary Let

Algorithm and Numerical example