关于矩阵方程(AX,XC)=(B,D)的对称解

On the Symmetric Solutions of Matrix Equation (AX, XC)=(B, D)

借助于矩阵的广义逆 ,给出了线性矩阵方程 (AX ,XC) =(B ,D)有对称解的充分必要条件 ;在有解的情况下 ,给出了通解的显式表示 ;作为特例 ,讨论了一类逆特征值问题。

By means of generalized inverses of matrices, a necessary and sufficient condition for matrix equation (AX, XC)=(B, D) having symmetric solutions is obtained, the explicit representation of general solution is given. As a special case, a class of inverse eigenvalue problem is also discussed.