线性流形上矩阵方程(A^TXA,B^TXB)=(C,D)的反对称解

The Skew-Symmetric Solution of the Linear Matrix Equation(A^TXA, B^TXB)=(C,D)On The Linear Manifold

本文利用矩阵对的商奇异值分解(QSVD),得到了线性流形上矩阵方程(A^T XA,B^T XB)=(C,D)反对称解存在的充分必要条件,并给出了通解表达式,同时解决了线性流形上此方程的最小二乘反对称解的通解表达式。

Using the guotient singular value decomposition（QSVD） of a matrix pair, this paper obtaines the necessary and sufficient conditions for the existence of and the expressions for the skew-symmetric solution and for the least-squares skew-symmetric solution of the linear matrix equation （A^TXA, B^TXB） = （C,D） on the linear manifold.