The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: a survey
type: Item
instance of: scholarly article
title: The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: a survey
zbMATH Open document ID: 0613.15017
DOI: 10.1016/0024-3795(86)90313-7
author: Hans Schneider
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The author gives a survey, beginning with Frobenius, of certain properties of a nonnegative matrix which are related to, or can be expressed by, properties of the marked reduced graph of the matrix. For a nonnegative square matrix P with Perron-Frobenius root \(\rho\) the areas surveyed are: (1) positivity properties of the eigenvectors and generalized eigenvectors of P; (2) the nonnegative solutions x of \((\lambda I-P)x=b\), for a given nonnegative vector b and given real number \(\lambda\) ; (3) the Jordan blocks associated with \(\rho\) in the Jordan canonical form of P; (4) the growth of the elements of \(P^ m\) as m grows.
reviewed by: Fergus J. Gaines
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 3991702
zbMATH Keywords: marked reduced graph
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: Perron-Frobenius root
zbMATH Keywords: positivity
zbMATH Keywords: eigenvectors
zbMATH Keywords: Jordan canonical form
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90313-7
OpenAlex ID: W2156502660
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description: scientific article; zbMATH DE number 3991702