3阶Hessenberg符号模式矩阵允许代数正和要求代数正
Hessenberg Sign Pattern Matrices with Order 3 that Allow Algebraic Positivity and Require Algebraic Positivity
摘要: 本文将引入Hessenberg符号模式矩阵的概念，通过对Hessenberg符号模式矩阵的研究，将所有3阶Hessenberg符号模式矩阵进行分类。分别给出不是允许代数正、允许代数正、允许代数正且要求代数正的等价条件。
Abstract: In this paper, we introduce the concept of Hessenberg sign pattern matrix. Through the study of Hessenberg sign pattern matrices, we classify all Hessenberg sign pattern matrices with order 3. We give three equivalent conditions on Hessenberg sign pattern matrices that do not allow algebraic positivity, allow algebraic positivity, and allow algebraic positivity and require algebraic positivity respectively.
文章引用：焦旸, 田岩. 3阶Hessenberg符号模式矩阵允许代数正和要求代数正[J]. 应用数学进展, 2022, 11(8): 5293-5300. https://doi.org/10.12677/AAM.2022.118556

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