矩阵方程AXB=C的解的存在唯一性及其数值分析

Existence,Uniqueness and Numerical Analysis of Solution for Matrix Equation AXB=C

利用Kronecker乘积,给出了矩阵方程AXB=C存在唯一解的充要条件,并对方程的解进行了扰动分析,最后给出了求良态方程近似解的一个数值方法及其应用实例.

Based on the Kronecker product of matrices,sufficient and necessary conditions for existence and uniqueness of solution for matrix equation AXB=C are obtained in this paper.Further,the perturbation analysis of the solution to these problems is carried out.Finally,the numerical simulation method for well-conditioned equation and its application are presented.