关于矩阵方程XB=C的解

本文推广了线性方程组反问题,讨论更一般的矩阵方程XB=C,分别给出这类方程存在对称矩阵解、正定对称矩阵解以及正交矩阵解的判定条件、解集合的结构及其一般解法,较完整地解决了线性方程组反问题与矩阵反问题。

On the Solutions of Matrix Equations XB=C

This paper generalizes the converse problems of simultaneous linear equations, discusses more general matrix equations XB=C, and gives criterion conditions under which this class of equations has symmetric matrix solutions, positive definite symmetric matrix solutions, and orthogonal matrix solutions, respectively. It also gives the structure of the solution set and the method to find the solutions. This paper solves the converse problems of simultaneous linear equations and matrix.