矩阵方程 (A^TXA,B^TXB=(C,D)的反对称解及其最佳逼近

The Anti-symmetric Solutions of the Matrix Equation (A^TXA,B^TXB)=(C,D) and its Optimal Approximation

本文利用矩阵对的标准相关分解 ,得到了矩阵方程 (ATXB,BTXB) =(C,D)反对称解存在的充分必要条件及通解表达式 。

By applying the canonical correlation decomposition (CCD) of matrix pairs,the necessary and sufficient conditions for the existence of and the general expression of the anti-symmetric solution of the matrix equation (A TXA,B TXB)=(C,D) are given.In addition,the optimal approximation anti-symmetric solution is obtained.