Let be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation . We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation.

中文翻译：

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指数为2的幂等矩阵的Yang-Baxter-Like矩阵方程的所有解

设指数为2的幂等矩阵，并考虑类似Yang-Baxter的矩阵方程。我们首先获得一个较小尺寸的矩阵方程组，以查找原始矩阵方程的所有解。当是秩为1和秩为2的幂零矩阵时，我们得到了杨-巴特矩阵方程的所有解。