矩阵方程AXB-CXD=R的多项式解法

Solution of matrix equation AXB-CXD=R with polynomial transformation

将利用线性变化,构造一多项式,从而将矩阵方程AXB-CXD=R转化为一容易求解的方程,并给出了矩阵方程AXB-CXD=R有唯一解时的显示表达式X=-(Ck+1)-1Sk(R)E-1或X=F-1Sk(R)(Bk+1)-1,所得到的结果推广了有关文献的相关结论.

Using the linear transformations to construct a polynomial,we change the matrix AXB-CXD=R into a new matrix equation,which could be soluted in easy.When the matrix equation AXB-CXD = R has a unique solution,we can give the unique solution X=-（C^k＋1）^-1Sk（R）E^-1or X=F^-1Sk（R）（B^k＋1）^-1 These results develop that in some papers.