利用矩阵的初等变换求方阵的特征值

The Solution for Eigenvalue of Square Matrices Using Elementary Transformation

高阶方阵的特征多项式以及特征值的求得,在计算上往往有一定的难度.本文首先从理论上分析了存在一个上三角矩阵或者下三角矩阵与一个方阵相似;接着,提出了相似变换的概念,分析了相似变换中初等矩阵的选择方法;然后指出了利用相似变换在求方阵的特征多项式以及特征值时的方法,并列举若干实例给予了说明.

To solve the characteristic polynomial and the eigenvalues of square matrices with higher order normally is not an easy way. In this paper, first, we analysis that there is an upper triangular matrix or a lower triangular matrix which is similar to a square matrix. Then, the concept of similar transactions is proposed, and the chosen way of elementary matrices about similar transaction is analysised. Then the methods for solving the characteristic polynomial and the eigenvalues of square matrices using similar transactions are showed, and several examples are given.