华东师范大学学报（自然科学版） >

2024 , Vol. 2024 >Issue 2: 23 - 29

DOI: https://doi.org/10.3969/j.issn.1000-5641.2024.02.003

数学

几类允许代数正的符号模式矩阵

  • 田岩 ,
  • 焦旸 ,
  • 于浩然
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  • 1. 辽宁师范大学 数学学院, 辽宁 大连　116029
    2. 吉林大学 数学学院, 长春　130012

收稿日期: 2022-09-11

  网络出版日期: 2024-03-18

基金资助

国家自然科学基金(12001225); 辽宁省教育厅自然科学研究青年项目(LQ2020021)

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Several classes of sign pattern matrices that allow algebraic positivity

  • Yan TIAN ,
  • Yang JIAO ,
  • Haoran YU
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  • 1. School of Mathematics, Liaoning Normal University, Dalian, Liaoning 　116029, China
    2. School of Mathematics, Jilin University, Changchun　130012, China

Received date: 2022-09-11

  Online published: 2024-03-18

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摘要

考虑三对角符号模式矩阵和爪形符号模式矩阵, 讨论了三对角符号模式矩阵和爪形符号模式矩阵是否允许代数正. 借助组合矩阵论和图论的方法, 给出了这两类符号模式矩阵允许代数正的必要条件. 最后, 分别给出了$n $阶三对角符号模式矩阵和$n $阶爪形符号模式矩阵允许代数正的等价条件.

关键词： 符号模式矩阵; 允许代数正; 三对角符号模式矩阵; 爪形符号模式矩阵

本文引用格式

田岩 , 焦旸 , 于浩然 . 几类允许代数正的符号模式矩阵[J]. 华东师范大学学报（自然科学版）, 2024 , 2024(2) : 23 -29 . DOI: 10.3969/j.issn.1000-5641.2024.02.003

Abstract

Tridiagonal sign pattern matrices and paw form sign pattern matrices were analyzed with respect to their potential for ensuring algebraic positivity. The necessary conditions allowing algebraic positivity of the two classes of sign pattern matrices were given using combinatorial matrix theory and graph theory. Finally, the equivalent conditions that would ensure algebraic positivity of tridiagonal sign pattern matrices and paw form sign pattern matrices of order $n $ were determined.

Key words： sign pattern matrix; allow algebraic positivity; tridiagonal sign pattern matrix; paw form sign pattern matrix

参考文献

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