一类特殊符号矩阵秩的研究

发布时间：2018-03-17 06:37

本文选题：符号矩阵　切入点：紧密交替符号矩阵　出处：《中北大学》2017年硕士论文　论文类型：学位论文

【摘要】：符号矩阵是符号模式矩阵的一个构成部分,对符号矩阵秩的研究属于组合矩阵论的研究领域。一个交替符号矩阵是指一个没有完全零行和零列的方阵,其元素取自于集合{+1,-1,0},且满足在任一行和任一列之中+1和-1交替出现,出现位置首元和末元都是+1。一个矩阵被称为紧密的是指它的每条线(行、列)上没有零元素存在于两个非零元素间。将符号矩阵A中的0元素换为1,1和-1换为0,获得的一个(0,1)矩阵B叫做A的补矩阵。本文主要研究了一类特殊符号矩阵——紧密交替符号补矩阵,全面探讨了它的秩的求解过程。文章的开头主要介绍了符号矩阵秩的研究背景、相关概念和研究现状。另外,还给出了本论文的主要结论。接下来给出了本文的主要研究内容,包括以下几个部分:第一部分:研究了紧密交替符号补矩阵的秩的分段求解过程。第二部分:提出了当n≥5k时,紧密交替符号补矩阵秩的计算算法并给出了几个实例验证了算法的可行性。第三部分:给出了该矩阵秩的程序实现结果。
[Abstract]:Symbol matrix is a component of symbol pattern matrix. The research on rank of symbol matrix belongs to the field of combinatorial matrix theory. An alternating symbol matrix refers to a square matrix with no complete zero rows and zero columns. Its elements are taken from the set {1n + 1 + 0} and satisfy the alternating occurrence of 1 and 1 in any row and column. The first and last elements of the occurrence position are 1. A matrix is called tight to refer to each line (row, line, line, line, line, line, line, line, line, line, line, line, line, line, line, line, line, line, line, line, line, No zero element exists between two non-zero elements on the column. The zero element in symbol matrix A is changed to 1 + 1 and 1 to 0, and the obtained matrix B is called a complement matrix of A. In this paper, a special type of symbol matrix is studied. -tight alternating symbolic complement matrix, At the beginning of this paper, the research background, related concepts and research status of the rank of sign matrix are introduced. In addition, the main conclusions of this paper are given. Then, the main research contents of this paper are given. It includes the following parts: in the first part, we study the piecewise solution of the rank of compact alternating sign complement matrix. The algorithm for calculating the rank of compactly alternately signed complementary matrices is given and several examples are given to verify the feasibility of the algorithm. Part three: the program implementation results of the rank of the matrix are given.
【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

【相似文献】