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 |
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.
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