The peripheral spectrum of a nonnegative matrix
type: Item
instance of: scholarly article
title: The peripheral spectrum of a nonnegative matrix
zbMATH Open document ID: 1022.15009
DOI: 10.1016/S0024-3795(02)00616-X
published in: Linear Algebra and its Applications
publication date: 2003-05-04T00:00:00Z
review text: A link between the Tam-Schneider condition [cf. \textit{B.-S. Tam} and \textit{H. Schneider}, Trans. Am. Math. Soc. 343, 479-524 (1994; Zbl 0826.15015)] on the peripheral spectrum of a nonnegative matrix \(A\), to the peripheral spectrum of the submatrix of \(A\) associated with the highest level set (levels are taken with respect to the spectral radius) is established. By extending this condition to all level sets, new necessary conditions on the Jordan form of the peripheral spectrum are provided and using a construction method for eventually nonnegative matrices it is shown that these conditions are also sufficient.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 1903569
zbMATH Keywords: peripheral spectrum
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: Jordan form
author: J. J. McDonald
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1903569