Abstract Let A be a square matrix satisfying A 4 = A {A}^{4}=A . We solve the Yang-Baxter-like matrix equation A X A = X A X AXA=XAX to find some solutions, based on analysis of the characteristic polynomial of A and its eigenvalues. We divide the problem into small cases so that we can find the solution easily. Finally, in order to illustrate the results, two numerical examples are presented.

中文翻译：

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Yang-Baxter-like矩阵方程的一些非交换解

摘要 设 A 为满足 A 4 = A {A}^{4}=A 的方阵。基于对A的特征多项式及其特征值的分析，我们求解Yang-Baxter-like矩阵方程AXA = XAX AXA=XAX以找到一些解。我们将问题分成小案例，以便我们可以轻松找到解决方案。最后，为了说明结果，给出了两个数值例子。