几类特殊矩阵的性质的探讨（本科）毕业论文.doc

几类特殊矩阵的性质的探讨 摘要 随着特殊矩阵的应用越来越广泛，人们对特殊矩阵的性质的研究也越来越深入。相应的，越来越多有关特殊矩阵的论文和期刊也层出不穷的发表。 本文主要具体分析了四种特殊矩阵：伴随矩阵、型矩阵、正交矩阵、幂零矩阵。论文的具体展开如下： 第一章主要介绍特殊矩阵的背景以及发展状况，加深了我对特殊矩阵的进一步认识；第二章讲述了一些预备知识，为下文的展开打下基础；第三章到第六章主要具体的介绍四类特殊矩阵：通过对它们的基本定义和基本性质进行深入研究并加以证明，我得到了很多有意义的结论，并将有些结论加以推广，以加深我对特殊矩阵更深层次的认识，最后对部分性质加以应用，使我对这些性质有了更好的掌握；最后一章对本文做了小结，并对特殊矩阵的研究加以展望。 特殊矩阵的研究是一个漫长的过程。对于特殊矩阵的研究只有通过大家的共同努力才能使特殊矩阵的理论更加完善，知识更加系统。 关键词：特殊矩阵；伴随矩阵；型矩阵；正交矩阵；幂零矩阵 THE DISCUSSION OF THE PROPERTIES ABOUT SEVERAL KINDS OF SPECIAL MATRIX ABSTRACT The study on the properties of special matrix is becoming more and more deeply with the application of special matrix becoming more and more widely.Accordingly, more and more papers and journals about the special matrix has been also published. This article mainly analyzes four kinds of special matrix: adjoint matrix, matrix,orthogonal matrix and nilpotent matrix.paper elaborated on the following: The first chapter mainly introduced the background and development status of special matrix.It deepened my further understanding of special matrix;The second chapter told the story of some preliminary knowledge in order to lay a foundation for the rest of the article.From the third chapter to the sixth chapter, I mainly introduced the four types of special matrix in detail:I got a lot of meaningful conclusion based on the in-depth study and proving about the basic definition and properties.I extended some conclusions to deepen my understanding of special matrix.To have a better master of these properties,I applied some natures finally.In the last chapter of this article,I made a summary, and I also did a research about the study of special matrix. The study of special matrix is a long process.In order to make special matrix theory be more perfect and the knowledge be more systematic,the only way is that we have to combine all of the efforts of the research on the special matrix. Key words: special matrix; adjoint matrix; matrix; orthogonal matrix; nilpotent matrix 目录 1 绪论………………..……