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.
Copyright Owner
The Author(s)
Copyright Date
2010
Language
en
File Format
application/pdf
Recommended Citation
Ellison, Elisabeth M.; Hogben, Leslie; and Tsatsomeros, Michael J., "Sign patterns that require eventual positivity or require eventual nonnegativity" (2010). Mathematics Publications. 245.
https://lib.dr.iastate.edu/math_pubs/245
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.