(AX,XC)=(B,D)的广义双对称解与广义双反对称解

The Generalized Bisymmetric Solution and Generalized Anti-bisymmetric Solution of(AX,XC)=(B,D)

设A,B是n×n阶矩阵,设C,D是n×m阶矩阵,研究了矩阵方程(AX,XC)=(B,D)具有广义双对称解和广义双反对称解的充要条件,并给出了矩阵方程(AX,XC)=(B,D)通解的表达式.

Let A,B be a n × n matrix, Let C,D be a n × m matrix. In this paper, the necessary and sufficient conditions for the existence of and the expressions for the generalized bisymmetric solution and the generalized antibi symmetric solution of linear matrix equation （ AX, XC） = （ B, D） are given.