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Two characterizations of matrices with the Perron–Frobenius property

✍ Scribed by Abed Elhashash; Daniel B. Szyld

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 77 KB
Volume: 16
Category: Article
ISSN: 1070-5325
DOI: 10.1002/nla.658

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✦ Synopsis

Abstract

Two characterizations of general matrices for which the spectral radius is an eigenvalue and the corresponding eigenvector is either positive or nonnegative are presented. One is a full characterization in terms of the sign of the entries of the spectral projector. In another case, different necessary and sufficient conditions are presented that relate to the classes of the matrix. These characterizations generalize well‐known results for nonnegative matrices. Copyright © 2009 John Wiley & Sons, Ltd.

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