用初等变换法求矩阵的若当标准形

摘要

给出相似变换和初等相似变换的定义,证明了任一n阶矩阵都可经一系列初等相似变换得到若当形矩阵,并介绍了用初等相似变换求若当矩阵及其相关过渡矩阵的方法。%In this paper, the similarity transformation and elementary similarity transformation are defined. It is proved that Jordan matrix can be obtained from any matrix by a series of elementary similarity transformation. Meanwhile, a method for determining Jordan matrix and the relevant matrix by elementary similarity transformation is described.