On the perron root of irreducible matrices

Sławomir Stańczak, Marcin Wiczanowski, Holger Boche

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

This chapter deals with the Perron root of nonnegative irreducible matrices. Applications abound with nonnegative and positive matrices so that it is natural to investigate their properties. In doing so, one of the central problems is to what extent the nonnegativity (positivity) is inherited by the eigenvalues and eigenvectors. The principal tools for the analysis of spectral properties of irreducible matrices are provided by Perron–Frobenius theory. A comprehensive reference on nonnegative matrices is [4]. Some basic results are summarized in App. A.4. For more information about the Perron–Frobenius theory, the reader is also referred to [5, 6, 7].

Original languageEnglish
Title of host publicationFoundations in Signal Processing, Communications and Networking
PublisherSpringer Science and Business Media B.V.
Pages3-60
Number of pages58
DOIs
StatePublished - 2008
Externally publishedYes

Publication series

NameFoundations in Signal Processing, Communications and Networking
Volume3
ISSN (Print)1863-8538
ISSN (Electronic)1863-8546

Keywords

  • Irreducible Matrix
  • Large Deviation Principle
  • Nonnegative Matrice
  • Perron Root
  • Spectral Radius

Fingerprint

Dive into the research topics of 'On the perron root of irreducible matrices'. Together they form a unique fingerprint.

Cite this