矩阵方程AXB=C的相容性与用“初等变换法”解矩阵方程

The Compatibility of the Matrix Equation AXB=C and the Mothed of Using "Elementary Tansformation Method" in Solving the Matrix Equation AXB=C

本文给出矩阵方程AXB=C有解的充要条件,它可判定矩阵方程是否有解,同时也成为用"初等变换法"解矩阵方程时能够直接应用的理论根据.文中还给出用"初等变换法"求解矩阵方程的规范化方法,使"初等变换法"能够成为解矩阵方程AXB=C的一种完整的方法.

This paper discussed the theorem of deciding the compatibility of the matrix equation AXB=C, and the theorem basis in solving the matrix equation AXB=C by using 'elementary transformation method'. Thus 'the elementary transformation method' becomes a complete one in solving the matrix equation AXB=C. This method is easy to understand and master. The ealculation quantity can be greatly reduced by using this method.