Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

2-2010

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

19

First Page

108

Last Page

120

DOI

10.13001/1081-3810.1351

Abstract

Several necessary or sufficient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n ≥ 2, the minimum number of positive entries in an n×n sign pattern that allows eventual positivity is n+1, and to classify all 2×2 and 3×3 sign patterns as to whether or not the pattern allows eventual positivity. A 3 × 3 matrix is presented to demonstrate that the positive part of an eventually positive matrix need not be primitive, answering negatively a question of Johnson and Tarazaga.

Comments

This article is published as Berman, Abraham, Minerva Catral, Luz DeAlba, Abed Elhashash, Frank Hall, Leslie Hogben, In-Jae Kim et al. "Sign patterns that allow eventual positivity." The Electronic Journal of Linear Algebra 19 (2009): 108-120. DOI: 10.13001/1081-3810.1351 . Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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