矩阵的地对角化及其的应用.doc

实用标准文案 PAGE 精彩文档 实用标准文案 精彩文档 湖北民族学院理学院2016届 本科毕业论文(设计) 矩阵的对角化及其应用 学生姓名： 赵远安 学 号： 021241015 专 业： 数学与应用数学 指导老师： 刘先平 答辩时间： 2016.5.22 装订时间： 2016.5.25 A Graduation Thesis (Project) Submitted to School of Science, Hubei University for Nationalities In Partial Fulfillment of the Requiring for BS Degree In the Year of 2016 Diagonalization of the Matrix and its Applications Student Name: ZHAO Yuanan Student No.: 021241015 Specialty: Mathematics and Applied Mathematics Supervisor: Liu Xianping Date of Thesis Defense:2016.5.22 Date of Bookbinding: 2016.5.25 精彩文档 精彩文档 摘 要 矩阵在大学数学中是一个重要工具，在很多方面应用矩阵能简化描述性语言，而且也更容易理解，比如说线性方程组、二次方程等. 矩阵相似是一个等价关系，利用相似可以把矩阵进行分类，其中与对角矩阵相似的一类矩阵尤为重要，这类矩阵有很好的性质，方便我们解决其它的问题. 本文从矩阵的对角化的诸多充要条件及充分条件着手，探讨数域上任意一个阶矩阵的对角化问题，给出判定方法，研究判定方法间的相互关系，以及某些特殊矩阵的对角化，还给出如幂等矩阵、对合矩阵、幂幺矩阵对角化的应用. 关键词：对角矩阵，实对称矩阵，幂等矩阵，对合矩阵，特征值，特征向量，最小多项式 Abstract The matrix is an important tool in college mathematics, and can simplify the description language based on the application of matrix in many ways. So it is easier to understand in many fields, for example, linear equations, quadratic equations. In many characteristics, the matrix similarity is an very important aspect. We know that the matrix similarity is an equivalence relation by which we can classify matrix, the diagonal matrix is very important. This kind of matrix has good properties, and it is convenient for us to solve other problems, such as the application of similar matrix in linear space. In this paper, we first discuss many necessary and sufficient conditions of diagonalization of matrix and then give some applications of special matrix diagonalization. Key words: diagonal matrix，real symmetric matrix，idempotent matrix，involutory matrix，the eigenvaule，the feature vector，minimal polynomial  目 录 摘要………………………………………………………………………………………… = 1 \* ROMAN \* MERGEFORMAT I …………………………………………………………………………………… = 2 \* ROMAN \* MERGEFORMAT II 绪言……………………………………