Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2019; 56(2): 305-318

Online first article March 8, 2019      Printed March 1, 2019

https://doi.org/10.4134/BKMS.b171108

Copyright © The Korean Mathematical Society.

Potentially eventually positive broom sign patterns

Ber-Lin Yu

Huaiyin Institute of Technology

Abstract

A sign pattern is a matrix whose entries belong to the set $\{+, -, 0\}$. An $n$-by-$n$ sign pattern $\mathcal{A}$ is said to allow an eventually positive matrix or be potentially eventually positive if there exist at least one real matrix $A$ with the same sign pattern as $\mathcal{A}$ and a positive integer $k_{0}$ such that $A^{k}>0$ for all $k\geq k_{0}$. Identifying the necessary and sufficient conditions for an $n$-by-$n$ sign pattern to be potentially eventually positive, and classifying the $n$-by-$n$ sign patterns that allow an eventually positive matrix are two open problems. In this article, we focus on the potential eventual positivity of broom sign patterns. We identify all the minimal potentially eventually positive broom sign patterns. Consequently, we classify all the potentially eventually positive broom sign patterns.

Keywords: eventually positive matrix, broom sign pattern, checkerboard block sign pattern

MSC numbers: 15A48, 15A18, 05C50

Supported by: The author’s work are supported by the Natural Science Foundation of HYIT under grant number 16HGZ007

Stats or Metrics

Share this article on :

Related articles in BKMS