对几类模式矩阵谱任意性的研究

发布时间：2018-07-01 16:06

本文选题：模式矩阵 + 蕴含幂零性　；参考：《中北大学》2017年硕士论文

【摘要】：符号模式矩阵是组合数学中的一个重要课题,能够在生物学、经济学,甚至社会学中发挥其独特的作用。符号模式矩阵的研究包括:蕴含幂零性、谱任意性、惯量任意性、最小非零元个数等。随着对符号模式矩阵的深入探究,出现了一系列新的概念,如:零-非零模式、复符号模式、ray模式等。本论文结构如下:第一章,介绍了符号模式的研究背景和意义,以及一些定义和研究成果,并概述了本论文的主要结论。第二章,研究了一类新的符号模式,讨论了n为奇数、偶数时的不同情况,并分别用N-J和N-C方法对其谱任意性进行刻画,且证明了它是极小谱任意的。第三章,找到了一类新的复符号模式矩阵,并分析了其谱任意性和极小谱任意性。第四章,研究了一类零-非零模式矩阵,将非零元规定适当的符号或换为适当的复数,分别可得到一个极小谱任意符号模式矩阵和一个极小谱任意复符号模式矩阵。
[Abstract]:Symbolic pattern matrix is an important subject in combinatorial mathematics, which can play a unique role in biology, economics and even sociology. The study of symbol pattern matrix includes: nilpotency, spectral arbitrariness, inertia arbitrariness, minimum number of nonzero elements, etc. With the further exploration of symbol pattern matrix, a series of new concepts have emerged, such as zero-non-zero mode, complex symbol pattern ray pattern, etc. The structure of this thesis is as follows: chapter one introduces the background and significance of symbolic pattern, some definitions and research results, and summarizes the main conclusions of this paper. In chapter 2, we study a new type of symbolic pattern, discuss the different cases when n is odd and even, and use N-J and N-C methods to characterize its spectral arbitrariness, and prove that it is arbitrary in minimal spectrum. In chapter 3, we find a new type of complex symbol pattern matrix, and analyze its spectral arbitrariness and minimal spectral arbitrariness. In chapter 4, we study a class of zero-nonzero mode matrices. We can obtain a minimal spectrum arbitrary symbol pattern matrix and a minimal spectrum arbitrary complex symbol pattern matrix by defining appropriate symbols or changing the non-zero elements into appropriate complex numbers.
【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】：O157

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