三类含有2n个非零元的极小谱任意符号模式

发布时间：2018-06-04 10:00

本文选题：符号模式矩阵 + 蕴含幂零　；参考：《中北大学》2015年硕士论文

【摘要】：符号模式矩阵的研究是组合数学研究中的一个重要分支。最早研究的符号模式矩阵理论是在经济学中。符号模式矩阵的理论不仅仅在数学学科中有着十分重要的作用，而且它的一系列研究成果在经济学、生物学、计算机科学等领域中也有着极其广泛的应用。本论文主要是运用幂零-雅克比方法研究了三类极小谱任意符号模式矩阵，具体的内容安排如下：第一章介绍组合数学的研究历史及意义、符号模式矩阵的相关概念。第二章介绍了三种证明符号模式矩阵是谱任意的方法：构造法、幂零-雅克比方法和幂零-中心化方法。第三章给出了两类特殊符号模式矩阵，用幂零-雅克比方法证明了它们是谱任意符号模式矩阵，，并证明了它们是极小谱任意符号模式矩阵。第四章给出了另一类特殊符号模式矩阵，用幂零-雅克比方法证明了它是谱任意符号模式矩阵，并证明了它也是极小谱任意符号模式矩阵。
[Abstract]:The study of symbolic pattern matrix is an important branch of combinatorial mathematics. The first study of the theory of symbolic pattern matrix is in economics. The theory of symbolic pattern matrix is not only very important in mathematics, but also a series of research results in the fields of economics, biology, computer science and so on. It has an extremely wide range of applications.
In this paper, we use the nilpotent Jacobian method to study three kinds of minimal spectrally arbitrary sign pattern matrices.
The first chapter introduces the research history and significance of combinatorial mathematics, and the related concepts of sign pattern matrix.
In the second chapter, we introduce three kinds of methods to prove the sign matrix is spectrally arbitrary: construction method, nilpotent Jacobi method and nilpotent centralization method.
In the third chapter, two kinds of special symbol pattern matrices are given. It is proved by the nilpotent Jacobian method that they are arbitrary symbolic pattern matrices of the spectrum and prove that they are minimal spectral arbitrary pattern matrices.
In the fourth chapter, another kind of special symbol pattern matrix is given. It is proved by the nilpotent Jacobian method that it is an arbitrary symbol pattern matrix of the spectrum, and it is also proved that it is also an arbitrary symbol pattern matrix of minimal spectrum.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157

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