初等行变换在简化线性矩阵方程求解中的应用

Applications of Elementary Row Transformation in Solving Linear Matrix Equation

文章给出了线性矩阵方程中的一种新的解法。此方法利用初等行变换法化简常见的线性矩阵方程对应的特定矩阵,依据化简结果可同时得到非齐次线性矩阵方程的一个特解和对应的基础解系,从而可直接写出通解,并通过算例检验了初等行变换法的可行性、简便性和有效性。

The elementary row transformation for solving linear matrix equation is discussed in this paper. Firstly, from the theory viewpoint, some conclusions are drawn as follows： using elementary row transformation can not only judge whether the non-homogeneous linear matrix equation has its solution, but also obtain the general solution of compatible linear matrix equation simultaneously, which consist of a particular solution and the basic set of solutions of its homogeneous linear matrix equation. Finally, the feasibility and efficiency of the elementary row transformation methods are verified by several experiments.