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

98

Last Page

107

DOI

10.13001/1081-3810.1350

Abstract

It is shown that a square sign pattern A requires eventual positivity if and only if it is nonnegative and primitive. Let the set of vertices in the digraph of A that have access to a vertex s be denoted by In(s) and the set of vertices to which t has access denoted by Out(t). It is shown that A = [αij] requires eventual nonnegativity if and only if for every s, t such that αst = −, the two principal submatrices of A indexed by In(s) and Out(t) require nilpotence. It is shown that A requires eventual exponential positivity if and only if it requires exponential positivity, i.e., A is irreducible and its off-diagonal entries are nonnegative.

Comments

This article is published as Ellison, Elisabeth, Leslie Hogben, and Michael Tsatsomeros. "Sign patterns that require eventual positivity or require eventual nonnegativity." The Electronic Journal of Linear Algebra 19 (2010): 98-107. DOI: 10.13001/1081-3810.1350. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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