矩阵方程(XA,XB)=(C,D)的广义对称解

THE GENERAL SYMMETRIC SOLUTIONS OF MATRIX EQUATION (XA,XB)=(C,D)

定义了广义对称矩阵 ;运用矩阵的奇异值分解与广义逆矩阵 ,给出了矩阵方程 (XA ,XB) =(C ,D)有广义对称解的充要条件 。

A concept of General Symmetric Matrices was put given. The general symmetric solution of matrix equation XA=C, XB=D is considered. Neccessary and sufficient condition for the existence of such solution and their general forms are derived by using the sigular value decomposition and generalized of matrices.