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Perron's Eigenvector for Matrices in Distribution Problems


  • Begoña, Subiza

    () (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

  • José, Silva-Reus

    () (Instituto Interuniversitario de Desarrollo Social y Paz)

  • Josep E., Peris

    () (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)


In this paper we consider convex combinations of matrices that arise in the study of distribution problems and analyse the properties of Perron's eigenvalue, and its associated positive eigenvector. We prove that the components in the (normalized) associated positive eigenvector have a monotone behaviour in the unit interval [0;1]: Moreover, we prove that the eigenvalue maximizes at the middle point of the interval. Additional properties are provided.

Suggested Citation

  • Begoña, Subiza & José, Silva-Reus & Josep E., Peris, 2012. "Perron's Eigenvector for Matrices in Distribution Problems," QM&ET Working Papers 12-15, University of Alicante, D. Quantitative Methods and Economic Theory.
  • Handle: RePEc:ris:qmetal:2012_015

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    Perrons eigenvalue; Positive Eigenvectors; Stochastic matrices; Distribution Problems;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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