矩阵方程AXB=C的(R,S)反对称解

(R,S) Anti-symmetric solution of matrix equation AXB=C

利用矩阵的广义奇异值分解,得到了矩阵方程AXB=C有(R,S)反对称解的充要条件,并给出了一般解的表达式,在此基础上给出了最佳逼近解的表达式。

The necessary and sufficient conditions and general solutions for （R,S） anti-symmetric solution AXB = C are derived by using generalized singular-value decomposition. Morever, the optimal approximation solution is provided.