二次型的有定性及其应用大学大学生毕业论文（设计）.doc

本科毕业论文（设计） 题 目 二次型的有定性及其应用 院（系） 数学系 专 业 数学与应用数学 学生姓名 XXXXXX 学 号 指导教师 XXXX 职称 XXXX 论文字数 7000 完成日期: 年 月 日 巢湖学院本科毕业论文论文二次型的有定性及其应用 摘要 二次型的有定性是二次型中有重要地位的内容。二次型的有定性指的是二次型的正定性、半正定性、负定性、半负定性。该文章没有考虑复二次型情况，只分析了实二次型的正定性，半正定性以及它们在数学以及其他科学上的应用。该文章先介绍二次型的定义，以及正定性，半正定性的定义和性质以及一些相关定理的证明，接着举例说明实二次型的有定性（正定性、半正定性）在高等数学以及物理学等科学上的应用。该文分两部分，先是总结并给出了实正定二次型的性质定理，以此为基础，再论述出半正定二次型的相关性质、定理，并总结出了其在处理数学问题方面的应用。 关键字： 实二次型；正定性；正定性应用；半正定性；半正定定性应用 The qualitative matrix and its application Abstract Definiteness of quadratic form holds an important position in quadratic form. The definiteness of quadratic form refers to positive definite, positive simi-definite, negative definiteness , negative simi-definite in quadratic form. In this paper, It did not take complex quadratic form into account, but analyzing the positive definiteness ,positive simi-definite of real quadratic form and their roles in mathematics and other scientific applications. This paper introduced the definition of the quadratic form ,along with the definition and the properties of the positive definiteness, positive simi-definite and some proof of relevant theorem at first ,then illustrate the real quadratic form arequalitative(positive qualitative, positive simi-definite)in advanced mathematics, physics and others scientific applications. This paper is divided into two parts, firstly , it summarized and given the properties of the real positive definite quadratic form theorem, as a basis, and then discusses the related properties ,theorem of positive semi-definite quadratic form , and summed up their applications in dealing with math problems . Keywords: Real quadratic form, positive definiteness, applications of positive definiteness, semi-positive definite, semi-definite qualitative applications 目 录 中文摘要 Ⅰ 英文摘