线性矩阵方程:AXB+CYD=F的递推解法

The Successive Substitution Method of Solving Matrix Equation AXB+CYD=F

解矩阵方程是一个有很强应用背景的传统问题. 应用广义逆矩阵和简单矩阵方程:AX=B,XC=D的求解方法,探索线性矩阵方程:AXB+CYD=F 的求解问题.

To solve matrix equation is a classical problem. This paper begins with the solving of the type of matrix equation AX=B, XC=D. With the successive substitution method, it then studies the ways of solving the matrix equation AXB+CYD=F. Finally, it gives the sufficient and necessary conditions with which AXB+CYD=F is solvable, and the general solutions of AXB+CYD=F are found out.