可约符号模式的惯量刻画

发布时间：2019-01-09 07:32

【摘要】：符号模式矩阵是组合矩阵论中一个重要的分支,符号模式矩阵理论主要研究符号模式矩阵所确定的定性矩阵类的组合性质,在组合矩阵论、图论、矩阵分析、常微分方程、算法理论中应用广泛。在《Matrices of Sign-solvable Linear Systems》一书中R.A.Brualdi和B.L.Shader系统总结了到1995年为止这一领域中所取得的研究成果,为之后的发展奠定了基础,将本课题的研究推向一个新的高度。自那之后出现了大量关于符号模式矩阵的研究文章并且产生了许多新概念如复模式、ray模式等。本文主要对惯量任意的可约符号模式进行了研究。第1章概述符号模式矩阵研究的起源、发展,介绍一些基本知识,提出本文的工作。第2章介绍矩阵惯量的几类重要性质及惯量研究的动态。第3章介绍一类特殊的惯量任意符号模式,即可约的惯量任意符号模式。完全刻画了4、5、6阶可约惯量任意符号模式。
[Abstract]:Symbolic pattern matrix is an important branch of combinatorial matrix theory. The symbolic pattern matrix theory mainly studies the combinatorial properties of qualitative matrix classes determined by symbolic pattern matrix, in combination matrix theory, graph theory, matrix analysis, ordinary differential equation, The algorithm theory is widely used. In "Matrices of Sign-solvable Linear Systems", R.A.Brualdi and B.L.Shader system summarize the research results in this field up to 1995, and lay the foundation for the later development, and push the research of this subject to a new height. Since then, there have been a lot of research papers on symbol pattern matrix and many new concepts such as complex schema, ray schema and so on have emerged. In this paper, we mainly study the reducible sign pattern with arbitrary inertia. Chapter 1 summarizes the origin and development of symbolic pattern matrix, introduces some basic knowledge, and puts forward the work of this paper. Chapter 2 introduces some important properties of matrix inertia and the dynamics of inertia research. In chapter 3, we introduce a class of special arbitrary symbol patterns of inertia, namely reduced arbitrary symbolic patterns of inertia. In this paper, arbitrary symbolic patterns of order 4 ~ 5 ~ 6 reducible inertia are completely characterized.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21

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