矩阵方程AX=XB的HERMITE解

HERMITIAN SOLUTIONS TO THE MATRIX EQUATION AX=XB

本文给出了矩阵方程有Hermite解,Hermite半正定解和Hermite正定解的必要且充分条件,并给出了解的表达式。

In this paper the author gives a necessary and sufficient condition for the existence of a Hermitian solution,positive semidefinite Hermitian Solution and positive definite Hermitian solution of the matrix equation AX=XB. He also gives the expressions of the solutions.