Testing the irreducibility of nonsquare Perron-Frobenius systems

C. Avin, M. Borokhovich, Y. Haddad, E. Kantor, Z. Lotker, M. Parter, D. Peleg

Research output: Contribution to journalArticlepeer-review

Abstract

The Perron-Frobenius (PF) theorem provides a simple characterization of the eigenvectors and eigenvalues of irreducible nonnegative square matrices. A generalization of the PF theorem to nonsquare matrices, which can be interpreted as representing systems with additional degrees of freedom, was recently presented in [1]. This generalized theorem requires a notion of irreducibility for nonsquare systems. A suitable definition, based on the property that every maximal square (legal) subsystem is irreducible, is provided in [1], and is shown to be necessary and sufficient for the generalized theorem to hold. This note shows that irreducibility of a nonsquare system can be tested in polynomial time. The analysis uses a graphic representation of the nonsquare system, termed the constraint graph, representing the flow of influence between the constraints of the system.

Original languageEnglish
Pages (from-to)728-733
Number of pages6
JournalInformation Processing Letters
Volume114
Issue number12
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Algorithms
  • Irreducibility
  • Perron-Frobenius theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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