The Perron-Frobenius theorem

Unnikrishna Pillai, Torsten Suel, Seunghun Cha

Research output: Contribution to journalArticle

Abstract

The Perron-Frobenius theorem provides a simple characterization of the eigenvectors and eigenvalues of some types of matrices with nonnegative entries. The importance of the theoreom stems from the fact that eigenvalue problems on these types of matrices arise in different fields of science and engineering. Some of the more common applications of the theorem are in considering the steady state behavior of Markov chains, power control in wireless networks, commodity pricing models in economics, population growth models, and Web search engines.

Original languageEnglish (US)
Pages (from-to)62-75
Number of pages14
JournalIEEE Signal Processing Magazine
Volume22
Issue number2
DOIs
StatePublished - 2005

Fingerprint

Perron-Frobenius Theorem
Population Growth
Eigenvalues and Eigenvectors
Web Search
Power Control
Population Model
Search engines
Growth Model
Search Engine
Eigenvalues and eigenfunctions
Power control
Markov processes
Pricing
Eigenvalue Problem
Wireless Networks
Wireless networks
Markov chain
Non-negative
Economics
Engineering

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

The Perron-Frobenius theorem. / Pillai, Unnikrishna; Suel, Torsten; Cha, Seunghun.

In: IEEE Signal Processing Magazine, Vol. 22, No. 2, 2005, p. 62-75.

Research output: Contribution to journalArticle

Pillai, Unnikrishna ; Suel, Torsten ; Cha, Seunghun. / The Perron-Frobenius theorem. In: IEEE Signal Processing Magazine. 2005 ; Vol. 22, No. 2. pp. 62-75.
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