Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

1-2012

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

23

First Page

1

Last Page

10

DOI

10.13001/1081-3810.1502

Abstract

A new class of sign patterns contained in the class of sign patterns that allow eventual nonnegativity is introduced and studied. A sign pattern is potentially strongly eventually nonnegative (PSEN) if there is a matrix with this sign pattern that is eventually nonnegative and has some power that is both nonnegative and irreducible. Using Perron-Frobenius theory and a matrix perturbation result, it is proved that a PSEN sign pattern is either potentially eventually positive or r-cyclic. The minimum number of positive entries in an n x n PSEN sign pattern is shown to be n, and PSEN sign patterns of orders 2 and 3 are characterized.

Comments

This article is published as Catral, M., C. Erickson, L. Hogben, D. Olesky, and P. Van Den Driessche. "Sign patterns that allow strong eventual nonnegativity." The Electronic Journal of Linear Algebra 23 (2012): 1-10. DOI: 10.13001/1081-3810.1502. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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