ALL SOLUTIONS OF THE YANG-BAXTER-LIKE MATRIX EQUATION WHEN A3 = A

Mansour Saeed Ibrahim Adam; Jiu Ding; Qianglian Huang; Lanping Zhu

doi:10.11948/2156-907X.20180244

2019 Volume 9 Issue 3

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Mansour Saeed Ibrahim Adam, Jiu Ding, Qianglian Huang, Lanping Zhu. ALL SOLUTIONS OF THE YANG-BAXTER-LIKE MATRIX EQUATION WHEN A3 = A[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 1022-1031. doi: 10.11948/2156-907X.20180244

Citation:

Mansour Saeed Ibrahim Adam, Jiu Ding, Qianglian Huang, Lanping Zhu. ALL SOLUTIONS OF THE YANG-BAXTER-LIKE MATRIX EQUATION WHEN A³ = A[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 1022-1031. doi: 10.11948/2156-907X.20180244

ALL SOLUTIONS OF THE YANG-BAXTER-LIKE MATRIX EQUATION WHEN A³ = A

1.
School of Mathematical Sciences, Yangzhou University, China
2.
Department of Mathematics, Faculty of Education, University of Khartoum P. O. Box 321, Sudan
3.
Department of Mathematics, University of Southern Mississippi, USA

Corresponding author: Email address: huangql@yzu.edu.cn(T. Feng)
Fund Project: The authors were supported by National Natural Science Foundation of China (11771378, 11871064) and the Yangzhou University Foundation for Young Academic Leaders (2016zqn03)

Abstract

Abstract

Let $A$ be a square matrix satisfying $A^3 = A$. We find all solutions of the Yang-Baxter matrix equation $AXA = XAX$, based on our previous result on all the solutions of the same equation for a matrix $A$ such that $A^2 = I$.
- Yang-Baxter-like matrix equation /
- diagonalizable matrix /
- eigenvalue
MSC: 92D05, 92D30, 34E10, 37H10

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