关于矩阵方程∑(from i=1 to n) A_iX_iB_i=F的可解性

THE SOLVABILITY ABOUD THE MATRIX EQUATIONni=1AiXiBi=F

本文考虑含有ｎ个未知矩阵Ｘ１，Ｘ２，Ｘ３，…，Ｘｎ的非齐次矩阵方程：Ａ１Ｘ１Ｂ１＋Ａ２Ｘ２Ｂ２＋…＋ＡｎＸｎＢｎ＝Ｆ，（１）其中Ａｉ∈Ｃｍ×ｌｉ，Ｂｉ∈Ｃｐｉ×ｑ，Ｘｉ∈Ｃｌｉ×ｐｉ，Ｆｉ∈Ｃｍ×ｑ．我们先给出一个求解的方法；然后利用矩阵的拉直运算和...

In this paper,we will consider the matrix equation with n unknown matrices X1,X2,…,Xnofni=1AiXiBi=FFirst,we will find out a method of the solution of the equation,then we will find out a necessary and safficient condition for the equation with solution by using the kronecker product and the matric operation