正定矩阵及其应用.doc

正定矩阵及其应用
本科毕业论文(设
学生姓名: 学号: 专业: 指导老师:
答辩时间: 装订时间:
计)
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
Positive definite matrices and their applications
Student Name: Student No.:
Specialty: Supervisor:
Date of Thesis Defense: Date of Bookbinding:
I
摘要
矩阵是高等代数里的一个基本概念,是代数知识的基础,是矩阵代数的一个主要研究对象. 它不仅是数学的一个重要分支,而且已经成为现在科技领域处理有限维空间形式与数量关系的强有力的工具. 而正定矩阵是从矩阵延伸出来的具有特殊性质的矩阵,是研究二次型的基础,在函数、不等式中都有应用,因此正定矩阵的特殊性质和广泛应用得到了许多学者
关注,进而对此进行了大量的研究. 本文从矩阵最基本的概念和性质出发,由浅入深,层层递进. 从矩阵的性质出发,给出了正定矩阵定义及其等价定义,归纳整理了正定矩阵的性质及其部分证明,总结了正定矩阵的判定定理,最后研究正定矩阵在理论证明和在函数极值中的应用.
关键词:矩阵正定二次型正定矩阵极值
I
Abstract
The matrix is very important in advanced algebra. It is not only an important branch, but also have e a powerful tool for studying finite dimensional space and quantity r- elationship in the real of modern science and technology. However , extending from the m- atrices, the positive definite matrix is a special matrix, which is a foundation for studying quadratic form and apply properly to both functions and inequality. Thus, its special prop- erty and wide applications have drawn scholars' attention, and a lot of research have been done. This paper begins with the matrix' primary concept and properties, going from the e- asy to the difficult. We define the positive definite matrix and its equivalent one, the sum up its properties and partial evidence, and summarize the determined theorems. At last, we study its application in theory and the solution of the function extremum.
Keywords: matrix, positive definite quadratic, positive definite matrix, extremum
II
目录
摘要.................................................................................................................................. I Abstract .................................................................................................................................. II