The Perron-Frobenius theorem: some of its applications

2005/03/01 by S.U. Pillai, Torsten Suel, T. Suel +1 · 14 citations
Physics and Astronomy · Computer Science · #Complex Network Analysis Techniques #Matrix Theory and Algorithms #Network Traffic and Congestion Control

paper · doi:10.1109/msp.2005.1406483

Abstract

The Perron-Frobenius theorem provides a simple characterization of the eigenvectors and eigenvalues of certain types of matrices with nonnegative entries. The importance of the Perron-Frobenius theorem stems from the fact that eigenvalue problems on these types of matrices frequently arise in many different fields of science and engineering. In this article, the authors discuss the applications of this theorem in diverse areas such as steady state behavior of Markov chains, power control in wireless networks, commodity pricing models in economics, population growth models, and Web search engines. The article starts with a review and discussion of the mathematical foundations.

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