Note on the Jordan form of an irreducible eventually nonnegative matrix

Main Article Content

Leslie Hogben
Bit-Shun Tam
Ulrica Wilson

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.

Article Details

Section
Article

Most read articles by the same author(s)