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Perron's Eigenvector for Matrices in Distribution Problems

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  • 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)

Abstract

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.

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Bibliographic Info

Paper provided by Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica in its series QM&ET Working Papers with number 12-15.

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Length: 18 pages
Date of creation: 26 Oct 2012
Date of revision:
Handle: RePEc:ris:qmetal:2012_015

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

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