矩阵乘法定理与线性矩阵方程

Matrix Multiplication Theorem and Linear Matrix Equation

为了更好地讨论线性矩阵方程的相容性,文章给出了矩阵乘法基本定理,并得到一系列关于矩阵方程相容性的推论。为了更好地揭示线性矩阵方程的通解的结构,文章讨论了左、右单位矩阵与矩阵的零因子与线性矩阵方程通解的关系,更科学地表述了非齐次线性矩阵方程与齐次线性矩阵方程的解的结构。

In order to achieve a better understanding of the compatibility of linear matrix equation,the paper puts forward the fundamental theorem of matrix multiplication,hence gains a seris of deduction about the compatibility of linear matrix equation.To reveal the general solution structure of linear matrix equation,the author discusses the relation between left and right identity matrix and zero divisor of matrix and the general solution of linear matrix equation,and expresses the solution structure of non-homogeneous and homogeneous linear matrix equation more scientifically.