Explicit solutions of the Yang-Baxter-like matrix equation for a singular diagonalizable matrix with three distinct eigenvalues
Duanmei Zhou, Xiang-Xing Ye, Qing‐Wen Wang, Jiawen Ding, Wenyu Hu · Filomat · 2021
Let A be a singular diagonalizable complex matrix with three distinct eigenvalues. We derive all explicit solutions X of the Yang-Baxter-like matrix equation AXA = XAX, by taking advantage of the Jordan form structure of A. The result generates the formula obtained in Chen et al. (2019) and M. Saeed Ibrahim Adam et al. (2019). We give examples to illustrate the validity of the results obtained in this paper.