4阶Hessenberg符号模式矩阵允许代数正
4-Order Hessenberg Sign Pattern Matrices That Allow Algebraic Positivity
DOI: 10.12677/AAM.2023.122061, PDF,    科研立项经费支持
作者: 焦 旸, 田 岩*：辽宁师范大学数学学院，辽宁 大连
关键词: 符号模式矩阵；Hessenberg符号模式矩阵；允许代数正；Sign Pattern Matrix； Hessenberg Sign Pattern Matrix； Allow Algebraic Positivity
摘要: 符号模式矩阵是组合矩阵论的一个重要研究热点，它在经济学、生物学、社会学等领域中具有广泛的应用。符号模式矩阵允许代数正是组合矩阵论中非常重要的问题，本文将考虑Hessenberg符号模式矩阵，通过对4阶Hessenberg符号模式矩阵的研究，给出4阶Hessenberg符号模式矩阵允许代数正的必要条件。4阶Hessenberg符号模式矩阵允许代数正的研究方法为其他特殊符号模式矩阵允许代数正的研究提供一定的思路和方法。
Abstract: The sign pattern matrix is an important research hotspot of combinatorial matrix theory. It is widely used in economics, biology, sociology and other fields. Sign pattern matrices that allow alge-braic positivity are a very important problem in combinatorial matrix theory. In this paper, we con-sider the Hessenberg sign pattern matrices. Through the study of Hessenberg sign pattern matrices with order 4, we give necessary conditions of 4-order Hessenberg sign pattern matrices that allow algebraic positivity. The research method of 4-order Hessenberg sign pattern matrices that allow algebraic positivity provides some ideas and methods for the research of other special sign pattern matrices that allow algebraic positivity.
文章引用：焦旸, 田岩. 4阶Hessenberg符号模式矩阵允许代数正[J]. 应用数学进展, 2023, 12(2): 582-589. https://doi.org/10.12677/AAM.2023.122061

参考文献

[1] Shan, H. and Shao, J. (2004) Matrices with Totally Signed Powers. Linear Algebra and Its Applications, 376, 215-224. [Google Scholar] [CrossRef] 
[2] Shao, J. (1999) On Sign Inconsistent Linear Systems. Linear Algebra and Its Applications, 296, 245-257. [Google Scholar] [CrossRef] 
[3] Shao, J. (2000) On the Digraphs of Sign Solvable Linear Systems. Linear Algebra and Its Applications, 33, 115-126. [Google Scholar] [CrossRef] 
[4] Shao, J. and Ren, L. (2004) Some Properties of Matrices with Signed Null Spaces. Discrete Mathematics, 279, 423-435. [Google Scholar] [CrossRef] 
[5] Shao, J. and Shan, H. (2002) The Solution of a Problem on Matrices Having Signed Generalized Inverses. Linear Algebra and Its Applications, 345, 43-70. [Google Scholar] [CrossRef] 
[6] Shao, J. and Shan, H. (2005) The Determinantal Regions of Complex Sign Pattern Matrices and Ray Pattern Matrices. Linear Algebra and Its Applications, 395, 211-228. [Google Scholar] [CrossRef] 
[7] Kirkland, S., Qiao, P. and Zhan, X. (2016) Algebraically Positive Matrices. Linear Algebra and Its Applications, 504, 14-26. [Google Scholar] [CrossRef] 
[8] Das, S. and Bandopadhyay, S. (2019) On Some Sign Patterns of Algebraically Positive Matrices. Linear Algebra and Its Appli-cations, 562, 91-122. [Google Scholar] [CrossRef] 
[9] Biswas, A. and Kundu, S. (2022) On Alge-braically Positive Matrices with Associated Sign Patterns. Resonance, 27, 1211-1235. [Google Scholar] [CrossRef] 
[10] Das, S. (2021) Classifications of Some Algebraically Positive, Diagonalizable and Stable Matrices with Their Sign Patterns. Department of Mathematics Indian Institute of Technology, Guwahati.
[11] Das S. (2022) Sign Patterns That Allow Algebraic Positivity. Linear Algebra and Its Applications, 653, 151-182. [Google Scholar] [CrossRef] 
[12] 詹兴致. 矩阵论[M]. 北京: 高等教育出版社, 2008.
[13] Brualdi, R.A. and Ryser, H.J. (1991) Combinatorial Matrix Theory. Cambridge University Press, New York, 55. [Google Scholar] [CrossRef] 

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