Uncoupling the Perron eigenvector problem
type: Item
instance of: scholarly article
title: Uncoupling the Perron eigenvector problem
zbMATH Open document ID: 0673.15006
DOI: 10.1016/0024-3795(89)90452-7
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: A method is given to find the unique normalized Perron vector \(\pi\) satisfying \(A\pi =\rho \pi\) where A is a nonnegative irreducible \(m\times m\) matrix with spectral radius \(\rho\), \(\pi =(\pi_ 1,-\pi_ m)^ T\) and \(\pi_ 1+...+\pi_ m=1\). The matrix is uncoupled into two or more smaller matrices \(P_ 1,P_ 2,...,P_ k\) such that this sequence has the following properties: (1) Each \(P_ i\) is irreducible and nonnegative and has a unique Perron vector \(\pi^{(i)}\). (2) Each \(P_ i\) has the spectral radius \(\rho\). (3) The Perron vectors \(\pi^{(i)}\) for \(P_ i\) can be determined independently. (4) The smaller Perron vectors \(\pi^{(i)}\) can easily be coupled back together to form the Perron vector \(\pi\) for A.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 4101376
zbMATH Keywords: Perron eigenvector
zbMATH Keywords: Perron complementation
zbMATH Keywords: nonnegative irreducible
zbMATH Keywords: matrix
author: Carl D. Meyer
reviewed by: Beate Ruffer-Henn
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90452-7
OpenAlex ID: W2009561564
cites work: Q3943082
cites work: Q4144754
cites work: Q3254327
cites work: Row Stochastic Matrices Similar to Doubly Stochastic Matrices
cites work: Matrix Analysis
cites work: Aggregation of Variables in Dynamic Systems
description: scientific article; zbMATH DE number 4101376