本文選題：符號模式矩陣 + 蘊含冪零��； 參考：《中北大學(xué)》2015年碩士論文

【摘要】：符號模式矩陣的研究是組合數(shù)學(xué)研究中的一個重要分支。最早研究的符號模式矩陣理論是在經(jīng)濟學(xué)中。符號模式矩陣的理論不僅僅在數(shù)學(xué)學(xué)科中有著十分重要的作用，而且它的一系列研究成果在經(jīng)濟學(xué)、生物學(xué)、計算機科學(xué)等領(lǐng)域中也有著極其廣泛的應(yīng)用。 本論文主要是運用冪零-雅克比方法研究了三類極小譜任意符號模式矩陣，具體的內(nèi)容安排如下： 第一章介紹組合數(shù)學(xué)的研究歷史及意義、符號模式矩陣的相關(guān)概念。 第二章介紹了三種證明符號模式矩陣是譜任意的方法：構(gòu)造法、冪零-雅克比方法和冪零-中心化方法。 第三章給出了兩類特殊符號模式矩陣，用冪零-雅克比方法證明了它們是譜任意符號模式矩陣，，并證明了它們是極小譜任意符號模式矩陣。 第四章給出了另一類特殊符號模式矩陣，用冪零-雅克比方法證明了它是譜任意符號模式矩陣，并證明了它也是極小譜任意符號模式矩陣。
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O157

【參考文獻】

相關(guān)期刊論文 前3條

1 李忠尚;INERTIA SETS OF SYMMETRIC SIGN PATTERN MATRICES[J];Numerical Mathematics A Journal of Chinese Universities(English Series);2001年02期

2 高玉斌;星符號模式的嵌套蘊含穩(wěn)定性[J];華北工學(xué)院學(xué)報;2003年06期

3 高玉斌;邵燕靈;;譜任意的符號模式矩陣(英文)[J];數(shù)學(xué)進展;2006年05期

本文編號：1976953