矩阵方程AX=B,XC=D的(M,N)-反对称解

The(M,N)-antisymmetric solutions of the matrix equations AX=B,XC=D

利用奇异值分解和广义奇异值分解,得到了矩阵方程AX=B,XC=D的(M,N)-反对称解存在的充要条件,给出了通解表达式及其最佳逼近问题的解,并提供了数值例子来说明理论结果的正确性.

In this paper,based on the singular value decomposition （SVD）of a matrix and the generalized singular value decomposition （GSVD）of a matrix pair,we establish the solvabili-ty conditions of matrix equations AX=B,XC=D for （M,N）-antisymmetric matrices,give the expressions of general solutions and the solution of corresponding optimal approximation problem,and give a numerical example to verify the correctness of the theoretical results.