矩阵的约当标准形及应用

On the Jordan canonical form of matrix and its application

复数域上矩阵的约当标准形是最常用的相似标准形,它圆满解决了复数域上矩阵的相似最简化问题,是线性代数理论中最深刻的内容之一,是线性代数的顶峰.回顾了矩阵约当标准形的理论背景和基本思想,研究了教学中值得注意的若干问题.列举3个实例探讨矩阵约当标准形的应用,从而加深对该理论的认识.

The Jordan canonical form of matrix is the most useful similarity standard form in the complex field,it satisfactorily solves the problem of similarity and simplification of matrices on the complex domain.It is one of the most profound contents of the linear algebra theory and the peak of linear algebra. Reviews the theoretical background and basic ideas of the Jordan canonical form of matrix,and studies several noteworthy issues in teaching.Finally,three examples are given to discuss the application of the Jordan canonical form of matrix,so as to deepen our understanding of the theory.