Some non-commuting solutions of the Yang-Baxter-like matrix equation-Reference-Cited by-同舟云学术

Some non-commuting solutions of the Yang-Baxter-like matrix equation

Published:2020-01-01 Issue:1 Volume:18 Page:948-969
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Zhou Duan-Mei¹²,Vu Hong-Quang²

Affiliation:

1. Department of Mathematics, Shanghai University , Shanghai , 200444 , People’s Republic of China

2. Department of Mathematics, College of Mathematics and Computer Science, Gannan Normal University , Ganzhou , 341000 , People’s Republic of China

Abstract

Abstract Let A be a square matrix satisfying

A 4 = A

{A}^{4}=A

. We solve the Yang-Baxter-like matrix equation

A X A = X A X

AXA=XAX

to find some solutions, based on analysis of the characteristic polynomial of A and its eigenvalues. We divide the problem into small cases so that we can find the solution easily. Finally, in order to illustrate the results, two numerical examples are presented.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0053/pdf

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