#### Campus Units

Mathematics

#### Document Type

Article

#### Publication Version

Published Version

#### Publication Date

6-2015

#### Journal or Book Title

Electronic Journal of Linear Algebra

#### Volume

30

#### First Page

279

#### Last Page

285

#### DOI

10.13001/1081-3810.3049

#### Abstract

A square complex matrix A is eventually nonnegative if there exists a positive integer k(0) such that for all k >= k(0), A(k) >= 0; A is strongly eventually nonnegative if it is eventually nonnegative and has an irreducible nonnegative power. It is proved that a collection of elementary Jordan blocks is a Frobenius Jordan multiset with cyclic index r if and only if it is the multiset of elementary Jordan blocks of a strongly eventually nonnegative matrix with cyclic index r. A positive answer to an open question and a counterexample to a conjecture raised by Zaslavsky and Tam are given. It is also shown that for a square complex matrix A with index at most one, A is irreducible and eventually nonnegative if and only if A is strongly eventually nonnegative.

#### Copyright Owner

The Author(s)

#### Copyright Date

2015

#### Language

en

#### File Format

application/pdf

#### Recommended Citation

Hogben, Leslie; Tam, Bit-Shun; and Wilson, Ulrica, "Note on the Jordan form of an irreducible eventually nonnegative matrix" (2015). *Mathematics Publications*. 232.

https://lib.dr.iastate.edu/math_pubs/232

## Comments

This article is published as Hogben, Leslie, Bit-Shun Tam, and Ulrica Wilson. "Note on the Jordan form of an irreducible eventually nonnegative matrix."

The Electronic Journal of Linear Algebra30 (2015): 279-285. DOI: 10.13001/1081-3810.3049. Posted with permission.