Jran标准形及其应用.doc

巢湖学院 本科毕业论文（设计） Jordan标准形及其应用 The Standard Jordan and Its Application 院（系） 数学系 专业 数学与应用数学 学生姓名 学号 指导教师 职称 论文字数 6987 完成日期: 2013年 月 日 矩阵的若尔当标准形是线性代数的一个重要组成部分，因为不是 每一个线性变换都有一组基使得它在这组基下的矩阵成为对角形，这 个时候为了探索在选择适当的基的情况下，一般的线性变换能化简成 什么形状，我们引入Y Jonton标准形。因为矩阵的JoRfon标准形具有结 构简单、易于计算等优点，在解决矩阵问题中起着很重要的作用，尤 其关于化矩阵为若尔当标准形的理论及方法，己经列为线性微分方程 组理论的必不可少的基础知识，例如利用若尔当标准形证明方阵的特 征根的性质，在计算矩阵多项式中的应用，在计算行列式中的应用， 在求解线性微分方程组的应用，现在我们着重讨论的是Jonton标准形 的理论和应用。 关键词：若尔当标准形；特征根；矩阵多项式；行列式 Abstract Jordan canonical form of matrix is an important part of linear algebra. It’s due to that not all linear transformation has a set of base which could make it in this group under the matrix become diagonal shape. In order to explore the linear transformation generally can be simplified into which kind of shape in the case of selecting the appropriate base, we introduced Jordan standard form. Since the canonical form of a matrix has the advantages of simple structure, easy to calculate and others, so it plays a very important role in solving the matrix problems, especially about the theory and method which could transform matrix into Jordan normal fornru For these reasonsjt has been listed as the essential foundation of knowledge to help solve the linear differential equations theory. Nowadays，the Jordan canonical form of matrix is extensively used in linear algebra，such as the character of using the Jordan standard form to proof the characteristic root of matrix，in addition，application in calculating the matrix polynomial，determinant and linear differential equation. Now what we will discuss emphatically is the theory of Jordan standard form and its application. Keywords: Jordan normal form， characteristic roots， matrix polynomial， determinant 目录 TOC \o 1-5 \h \z 巾文 I 英文 TT 弓 IB 1 HYPERLINK \l bookmark10 \o Current Document \h Jordan矩阵相关的定义定理 1 HYPERLINK \l bookmark11 \o Current Document \h 1 Jordan矩阵相关的定义 1 HYPERLINK \l bookmark12 \o Current Document \h 1.2 Jordan标准形相关的定理 3 HYPERLINK \l bookmark15 \o