SOLVING THE YANG-BAXTER-LIKE MATRIX EQUATION FOR A RANK-ONE MATRIX

Mohammed Ahmed Adam Abdalrahman; Jiu Ding; Qianglian Huang

doi:10.11948/20230115

2023 Volume 13 Issue 5

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Mohammed Ahmed Adam Abdalrahman, Jiu Ding, Qianglian Huang. SOLVING THE YANG-BAXTER-LIKE MATRIX EQUATION FOR A RANK-ONE MATRIX[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2987-2994. doi: 10.11948/20230115

Citation:

Mohammed Ahmed Adam Abdalrahman, Jiu Ding, Qianglian Huang. SOLVING THE YANG-BAXTER-LIKE MATRIX EQUATION FOR A RANK-ONE MATRIX[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2987-2994. doi: 10.11948/20230115

SOLVING THE YANG-BAXTER-LIKE MATRIX EQUATION FOR A RANK-ONE MATRIX

1.
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
2.
Department of Mathematics, Faculty of Science and Information Technology, University of Nyala, P. O. Box 63311, Sudan
3.
School of Mathematics and Natural Sciences, University of Southern Mississippi, Hattiesburg, MS 39406

Author Bio: Email: Mohammed.sudan112@gmail.com (M. A. A. Abdalrahman); Email: Jiu.Ding@usm.edu(J. Ding)
Corresponding author: Email: huangql@yzu.edu.cn(Q. Huang)
Fund Project: This research is supported by National Natural Science Foundation of China (11771378)

Abstract

Abstract

We reduce the problem of solving the Yang-Baxter-like matrix equation $ AXA = XAX $, where $ A $ is a rank-one matrix, to that of solving linear matrix equations, obtaining all solutions. We use a direct and unified approach for the both cases that $ A $ is diagonalizable or otherwise, instead of seeking the help of the Jordan canonical form or factorization of $ A $. Based on the characterizations for the solutions, we derive a perturbation result when $ A $ is not diagonalizable.
- Yang-Baxter-like matrix equation /
- nilpotent matrix /
- Moore-Penrose generalized inverse /
- perturbation
MSC: 15A18

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References

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