求广义特征向量的一种算法

An algorithm of Finding Extended Eigenvector

文章提出了初等相似变换的概念 ,探讨了如何利用初等相似变换法求一个方阵的Jordan标准形及变换矩阵 ,进而为求一个方阵的广义特征向量创造了条件。该算法对一些特殊方阵 ,求它的特征值、各级广义特征向量、Jordan标准形及变换矩阵 ,比用解方程组方法要简单。

In this paper, the concept of elementary transformation of similitude is proposed, and the method how to find the Jordan canonical form of a square matrix and its transformation matrix are studied. Thereby, favorable conditions of finding the extended eigenvector of square matrix are created. This algorithm is simplier than the method of using the solution of equations when it is used to find some special matrices' eigenvelue, extended eigenvector, Jordan canonical form and its transformation matrix.