矩阵方程AX=A+X有正定解和幂零解的充要条件

The Necessary and Sufficient Conditions of the Matrix Equation AX=A+X Existing Positive Definite Solution and Nilpotent Solution

给出了矩阵方程AX=A+X有解、实对称解、正定解和幂零解的充要条件.

The necessary and sufficient conditions are given for the matrix equation AX= A＋X has solutions, real symmetric solutions, positive definite solutions or nilpotent solutions.