Powers of Complex Persymmetric Antitridiagonal Matrices with Constant Antidiagonals

Haibo Wang

doi:10.1155/2014/451270

Abstract

We derive a general expression for the pth power (p∈N) of any complex persymmetric antitridiagonal Hankel (constant antidiagonals) matrices. Numerical examples are presented, which show that our results generalize the results in the related literature (Rimas 2008, Wu 2010, and Rimas 2009).

Highlights

Solving some difference, differential, and delay differential equations, we meet the necessity to compute the arbitrary positive integer powers of square matrix
We derive a general expression for the pth power (p ∈ N) of any complex persymmetric antitridiagonal matrices with constant antidiagonals (antitridiagn(b, a, b))
We study the entries of positive integer power of an n × n complex persymmetric antitridiagonal matrix with constant antidiagonals as follows: ba

Summary

Introduction

Differential, and delay differential equations, we meet the necessity to compute the arbitrary positive integer powers of square matrix. In 2013, Rimas [6] gave the eigenvalue decomposition for real odd order skew-persymmetric antitridiagonal matrices with constant antidiagonals (antitridiagn(a, b, a)) and derived the general expression for integer powers of such matrices. We derive a general expression for the pth power (p ∈ N) of any complex persymmetric antitridiagonal matrices with constant antidiagonals (antitridiagn(b, a, b)). This novel expression is both an extension of the one obtained by Rimas for the powers of the matrix antitridiagn(1, 0, 1) with n ∈ N (see [2] for the odd case and [5] for the even case) and an extension of the one obtained by Honglin Wu for the powers of the matrix antitridiagn(1, 1, 1) with n ∈ N (see [3] for the even case)

Derivation of General Expression

Numerical Examples

Conclusion and Discussion