4阶Hessenberg符号模式矩阵允许代数正  

4-Order Hessenberg Sign Pattern Matrices That Allow Algebraic Positivity

作　　者：焦旸 田岩 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2023年第2期582-589,共8页Advances in Applied Mathematics

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。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.

关 键 词：符号模式矩阵 Hessenberg符号模式矩阵 允许代数正 

分 类 号：O24[理学—计算数学]