矩阵方程AX+XBT=C唯一解的判定与求法

摘要

利用实矩阵的相似标准形对矩阵方程AX+ XBT =C的解的唯一性进行了探讨,得到了方程有唯一解的一个充要条件,并在有唯一解的条件下对如何求解进行了研究,得出了求得方程唯一解的一种简便方法.%In this paper, it discussed the uniqueness of solutions for the matrix equations AX +XBT = C by using the canonical forms of real martices, and we get the necessary and sufficient condition when the equation has a unique solution. Finally, we propose an algorithm to solve the matrix equa-tion under the conditions of a unique solution.