摘要
本文利用矩阵的 Frobenius 标准形讨论了矩阵方程 AX-XB=C 的解的情况,特别给出了该方程有解时的递推解法,同时给出了该方程有唯一解的充要条件的另一个证明。
In this paper,by using the Frobenius canonical form,the solution of the matrix equation AX-XB=C is thoroughly discussed.The recursive solving method is given in particular when this equation has role solution or solutions.In addition,another proof of the necessary and sufficient condition for the solution of this equation is supplied without using Kronecker multiplication.
关键词
矩阵方程
解
Kronecker multiplication
non-derogatory matrix
Frobenius canonical form
