双对称线性矩阵方程的最佳逼近解

本文讨论了wang和Chang的双线件矩阵方程(ATXA,BTXB):(C,D)对称解的一致性条件.利用Hilbert空间的投影定理、商奇异值分解及其通解表达式和典型相关分解(CCD)的有效工具,获得了关于这个矩形方阵对的最小二乘问题的明确的解析表达式反对称(或最小Frobenius范数反对称解作为特例)最佳逼近解.

THE ANTI-SYMMETRIC OPTIMAL APPROXIMATION SOLUTION FOR A LINEAR MATRIX EQUATION PAIR

This article discusses the consistent conditions of the symmetric solution and symmetric least squares solution for the linear matrix equation pair(ATXA,BTXB)=(C,D)obtained by Chang and Wang(1993).By using the projection theorem in Hilbert space,the quotient singular value decomposition(QSVD)and the canonical correlation decomposition(CCD)for efficient tools to obtain the explicit analytical expression of the anti-symmetric optimal approximation solution(or the minimum Frobenius norm anti-symmetric solution as a special case)for the least-squares problem of this matrix equation pair.