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On Hypothesis about the Second Eigenvalue of the Leontief Matrix


  • Stanisław Białas
  • Henryk Gurgul


If an arbitrarily positive eigenvector is repeatedly premultiplied by a positive matrix, then the result tends towards a unique, positive (Frobenius) eigenvector. Brady has demonstrated that the expected absolute magnitude of the estimate of the second largest eigenvalue of a positive random matrix (with identically and independently distributed entries) declines monotonically with the increasing size of the matrix. Hence, the larger the system is, the faster is the convergence. Molnar and Simonovits examined Brady's conjecture in the case where entries of a stochastic matrix are close to 1/n. We prove this hypothesis for any stochastic and positive matrix.

Suggested Citation

  • Stanisław Białas & Henryk Gurgul, 1998. "On Hypothesis about the Second Eigenvalue of the Leontief Matrix," Economic Systems Research, Taylor & Francis Journals, vol. 10(3), pages 285-290.
  • Handle: RePEc:taf:ecsysr:v:10:y:1998:i:3:p:285-290 DOI: 10.1080/762947113

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    Cited by:

    1. Theodore Mariolis & Lefteris Tsoulfidis, 2012. "On Brody’S Conjecture: Facts And Figures From The Us Economy," Discussion Paper Series 2012_06, Department of Economics, University of Macedonia, revised May 2012.
    2. Christian Bidard & Tom Schatteman, 2001. "The Spectrum of Random Matrices," Economic Systems Research, Taylor & Francis Journals, vol. 13(3), pages 289-298.

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    Equilibrium; second eigenvalue; convergence;


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