线性矩阵方程的有解条件和解的结构

Solution conditions of linear matrix equation and structure of solution

借助矩阵直积的性质和广义逆矩阵的结论,给出了线性矩阵方程有解的充要条件、解的结构和矩阵方程的极小范数最小二乘解。

By means of the propertics of matrix directory product and the conclusion of generalized inverse matrix,the paper gave the ample necessary conditions of linear matrix equation solution, the structure of the solution and the least square solution of extreme small matrixes of the matrix equation.