关于幂零矩阵的Yang-Baxter矩阵方程的所有解

All Solutions of the Yang-Baxter Matrix Equation for Nilpotent Matrix

令A是一个指数为2的幂零矩阵,本文给出了二次矩阵方程AXA=XAX的所有解的求解方法.当A是一个秩为1的幂零矩阵时,详细给出了方程AXA=XAX的所有解.

Let A be a nilpotent matrix with index 2.We obtain the method of finding all solutions of the quadratic matrix equation AXA=XAX.When A is a nilpotent matrix with rank 1,we get all solution of the equati AXA=XAX on in detail.