矩阵方程A^TXA+B^TYB=D及A^TXA=CB^TXB=D的对称解

The Symmetric Solutions of the Matrix Equations A^TXA+B^TYB=D and A^TXA=C, B^TXB=D

运用矩阵的奇异值分解与广义逆矩阵 ,给出了矩阵方程AT XA +BTYB =D及矩阵方程ATXA=C ,BT XB =D有对称解的充分必要条件 ,并在有解的情况下 。

The symmetric solutions of the matrix equtionsA TXA+B TYB=D and A TXA=C, B TXB=D are considered. Necessary and sufficient conditions for the existence of such solutions and their general forms are derived by using the singular value decomposition and generalized inverses of matrices.