文档介绍：本科毕业论文(设计)
题目低秩矩阵的特征多项式和最小多项式
姓名学号
专业年级数学与应用数学
指导教师职称

2009年4月20日
目录
绪论………………………………………………………………………………(1)
1 相关概念与记号…………………………………………………………………(1)
概念…………………………………………………………………………(1)
本文中相关记号……………………………………………………………(1)
2 矩阵的满秩分解…………………………………………………………………(2)
3 降阶求特征多项式………………………………………………………………(3)
4 降阶求最小多项式………………………………………………………………(5)
5 最小多项式的几种求法及比较…………………………………………………(9)
根据特征多项式求最小多项式……………………………………………(9)
根据不变因子求最小多项式……………………………………………(10)
根据Jordan标准形求最小多项式………………………………………(11)
根据线性相关求最小多项式……………………………………………(12)
最小多项式求法的综合比较……………………………………………(13)
6 最小多项式的简单应用………………………………………………………(14)
参考文献…………………………………………………………………………(16)
低秩矩阵的特征多项式与最小多项式
摘要
矩阵的特征多项式和最小多项式在矩阵相似、若当标准形、矩阵函数和矩阵方程中都有很重要的作用,,通过特殊情况下的满秩分解求出矩阵的特征多项式,再推广到一般,,同样得到了一种求最小多项式的降阶公式,,本文列举了目前已有的四种最小多项式的四种求法,并结合本文的最小多项式的求法作了一个综合的比较.
【关键词】矩阵满秩分解特征多项式最小多项式
The Characteristic Polynomial and the Minimal Polynomial
of the Low-rank Matrix
Abstract
The characteristic polynomial and the minimal polynomial play a great role in the matrix similarity, Jordan canonical form, matrix function, matrix equation. So how to seek them is very important. Firstly, from the full-rank position of the matrix, we can get the characteristic polynomial in the special case of full-rank position, and it is the same in the general case, so we get a method of seeking characteristic polynomial by reducing the order of the matrix. Then according to the definition of minimal polynomial of matrix and the principle of matrix multiplication, we also get a method of seeking minimal polynomial by reducing the order of the matrix. To a great extent, we have putation about the characteristic polynomial and the minimal polynomial of the low-rank matrix. Finally, we list the four exiting methods of seeking the minimal polynomial. Combining with the method of the minimal polynomial in the paper, we make