Principal submatrices of co-order one with the biggest Perron root
type: Item
instance of: scholarly article
title: Principal submatrices of co-order one with the biggest Perron root
zbMATH Open document ID: 1071.15010
published in: Linear Algebra and its Applications
publication date: 2004-11-22T00:00:00Z
review text: This paper concerns principal submatrices of co-order 1 with the largest Perron root. Results are given in spectral terms, but proved in graph-theoretic language. Accordingly, the paper begins by discussing maximal proper strong subdigraphs, Hamiltonian walks in extremal one-vertex-deleted subdigraphs and then turns to Perron-generated eigenvectors for principal submatrices of co-order 1 with the largest Perron root, and finally discusses some classes of irreducible matrices with irreducible principal submatrices of co-order 1 having the largest Perron root.
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 2117278
zbMATH Keywords: Irreducible nonnegative matrix
zbMATH Keywords: Principal submatrix of co-order one
zbMATH Keywords: Perron root
zbMATH Keywords: Strong digraph
zbMATH Keywords: One-vertex-deleted subdigraph
zbMATH Keywords: Hamiltonian circuit
zbMATH Keywords: Hamiltonian path
zbMATH Keywords: Hamiltonian walk
author: S. V. Savchenko
MaRDI profile type: Publication
full work available at URL: j.laa.2004.01.024
OpenAlex ID: W2002197359
cites work: Spectral properties of an indecomposable non-negative matrix and its principal submatrices of co-order one
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cites work: Perron components and algebraic connectivity for weighted graphs
DOI: 10.1016/J.LAA.2004.01.024
description: scientific article; zbMATH DE number 2117278