线性流形上矩阵方程A^TXA=B的D对称解

The D-symmetric Solutions of Matrix Equation A^TXA=B on the Linear Manifold

利用矩阵对的广义奇异值分解,给出线性流形上矩阵方程ATXA=B存在D对称解的充要条件及其通解的表达式,并导出线性流形上矩阵方程ATXA=B的D对称最小二乘解的表达式.

By applying the generalized singular value decomposition of a matrix pair, the necessary and sufficient conditions and the expressions for the D-symmetric solutions of matrix equation A^TXA = B on the linear manifold are established. In addition, the least-squares solutions of A^TXA=B with respect to D-symmetric matrix are derived.