符号模式矩阵若干性质的研究-计算数学专业论文.docxVIP

万方数据 万方数据 摘要 摘 要 符号模式矩阵最初是为了处理线性动力系统中的一些定性问题而提出的, 而 线性动力系统符号可解性及符号稳定性的研究是当时解决一些定性问题的重点. 由于符号模式矩阵在定性经济学中的重要应用以及作为线性代数、组合数学和图 论的交叉学科, 符号模式矩阵引起了经济学家、数学家以及计算机专家的广泛关注, 从而使符号模式矩阵理论成为组合矩阵论中的一个新兴研究领域. 本文大体分为 三个部分, 主要研究内容如下: 第一部分, 主要介绍了符号模式矩阵的产生背景, 给出了一般矩阵以及符号 模式矩阵的一些基本知识、相关结论及本文的主要结论; 第二部分, 通过研究符号模式矩阵对一些特殊矩阵的允许性, 给出符号模式 矩阵与 N ??矩阵、 P ??矩阵、 M ??矩阵、和逆 M ??矩阵允许的充要条件; 第三部分, 讨论了一类特殊符号模式矩阵的蕴含幂零、谱任意以及极小谱任意 性. 关键词：符号模式, 谱任意, 允许性, 蕴含幂零 I ABSTRACT ABSTRACT Sign pattern matrix was originally raised in order to deal with some qualitative questions in the linear dynamic system, and the research in Sign-solvable and sign-stability of the linear dynamic system was then a key point of solving some qualitative questions. As an interdiscipline of linear algebra, combinatorial mathematics and graph theory, sign pattern matrix has some important applications in the qualitative economic science. Just because of this, sign pattern matrix causes generally concern of the economist, mathematician and computer expert. Also, the theory of sign pattern matrix becomes an emerging research area in the combinatorial matrix theory. This thesis is mainly divided into three chapters, and its main contents are as follows: In the first part , the auther mainly introduce the background of sign pattern matrix. At the same time, the auther also introduce some basic knowledges and relevant conclusions of the general matrix and sign pattern matrix. Finally, the main conclusions of this thesis are given. In the second part , through researching the admissible properties for some special matrices of sign pattern matrix, some sufficient and necessary conditions are given. In the third part , we mainly discuss whether a new kind of sign pattern matrix is potentially nilpotent, spectrally arbitrary and minimal spectrally arbitrary. Keywords: sign pattern, spectrally arbitrary, admissibility, potentially nilpotent II 目录 目 录 HYPERLINK \l _bookmark0 第一章 绪 论 ......................................................1 HY