AxA＊=B的对称广义中心对称解

The Symmetric Generalized Centro-symmetric Solutions of AXA =B

复数域上矩阵方程AXA*=B的对称广义中心对称解.利用对称广义中心对称矩阵的特殊结构,将AXA*=B转化为等价的矩阵方程A1X1A1*+A2X2A2*=B,并利用该方程的Hermitian解得到AXA*=B的对称广义中心对称解存在的充要条件及通解表达式.

Abstract In this paper, we study the symmetric generalized centro-symmetric solutions of the ma- trix equation AXA=B. By applying the special structure of the symmetric generalized centro-symmet- ric matrix, we transform AXA=B into the equation A1X1A1＋A2X2A2=B. Then ws derive the nec- essary and sufficient conditions for the existence of such solutions and their general forms by using the Hermitian solutions of the latter equation.