矩阵方程A^TXA=B的D-对称解及其最佳逼近

Solutions of D-symmetric Matrices to Linear Matrix Equation A^TXA=B and Their Optimal Approximation

研究了方程ATXA=B的D-对称解及其最佳逼近问题.利用矩阵对的标准相关分解定理给出了矩阵方程ATXA=B在D-1SRn×n上相容的充分必要条件、解的一般表达式及其最佳逼近表达式.

In this paper,the solutions to ATXA=B for D-symmetric matrices and their optimal approximation are studied.By using a series of methods,including the canonical correlation decomposition of a pair of matrices,the generalized inverse of a matrix and so on,the general representation of the solutions and the expression of the optimal approximation are given.