Several classes of sign pattern matrices that allow algebraic positivity

doi:10.3969/j.issn.1000-5641.2024.02.003

Journal of East China Normal University(Natural Science) ›› 2024, Vol. 2024 ›› Issue (2): 23-29.doi: 10.3969/j.issn.1000-5641.2024.02.003

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Several classes of sign pattern matrices that allow algebraic positivity

Yan TIAN^1,*(), Yang JIAO¹, Haoran YU²

1. School of Mathematics, Liaoning Normal University, Dalian, Liaoning 　116029, China
2. School of Mathematics, Jilin University, Changchun　130012, China

Received:2022-09-11 Online:2024-03-25 Published:2024-03-18
Contact: Yan TIAN E-mail:tiantian8835@163.com

Abstract

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

CLC Number:

O151.21

Yan TIAN, Yang JIAO, Haoran YU. Several classes of sign pattern matrices that allow algebraic positivity[J]. Journal of East China Normal University(Natural Science), 2024, 2024(2): 23-29.

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Several classes of sign pattern matrices that allow algebraic positivity

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