Solving the Yang-Baxter-Like Matrix Equation For a Rank-One Matrix
Mathematics and Natural Sciences
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.
Journal of Applied Analyis and Computation
(2023). Solving the Yang-Baxter-Like Matrix Equation For a Rank-One Matrix. Journal of Applied Analyis and Computation.
Available at: https://aquila.usm.edu/fac_pubs/21553