矩阵的对角化及其应用（完整版）实用资料(可以直接使用，可编辑完整版实用资料，欢迎下载）学院2021届本科毕业论文(设计)矩阵的对角化及其应用学生姓名：学号：专业：数学与应用数学指导老师：AGraduationThesis(Project)SubmittedtoSchoolofScience,HubeiUniversityforNationalitiesInPartialFulfillmentoftheRequiringforBSDegreeIntheYearof2021DiagonalizationoftheMatrixanditsApplicationsStudentNameStudentNo.:Specialty:Supervisor:DateofThesisDefense:DateofBookbinding: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n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IAbstractThematrixisanimportanttoolincollegemathematics,andcansimplifythedescriptionlanguagebasedontheapplicationofmatrixinmanyways.Soitiseasiertounderstandinmanyfields,forexample,linearequations,quadraticequations.Inmanycharacteristics,thematrixsimilarityisanveryimportantaspect.Weknowthatthematrixsimilarityisanequivalencerelationbywhichwecanclassifymatrix,thediagonalmatrixisveryimportant.Thiskindofmatrixhasgoodproperties,anditisconvenientforustosolveotherproblems,suchastheapplicationofsimilarmatrixinlinearspace.Inthispaper,wefirstdiscussmanynecessaryandsufficientconditionsofdiagonalizationofmatrixandthengivesomeapplicationsofspecialmatrixdiagonalization.Keywords:diagonalmatrix，realsymmetricmatrix，idempotentmatrix，involutorymatrix，theeigenvaule，thefeaturevector，minimalpolynomialII目录摘要„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„IAbstract„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„II绪言„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„1课题背景„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„1目的和意义„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„1国内外概况„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„1预备知识„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„2相关概念„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„2矩阵的对角化„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„4特殊矩阵的对角化„„„„„„„„„„„„„„„„„„„„„„„„„„„14矩阵对角化的应用„„„„„„„„„„„„„„„„„„„„„„„„„„„22总结„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„24致谢„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„25参考文献„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„26独创声明„„„„„„„„„„„„„„„„„„