On Hypothesis about the Second Eigenvalue of the Leontief Matrix
AbstractIf 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.
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Bibliographic InfoArticle provided by Taylor and Francis Journals in its journal Economic Systems Research.
Volume (Year): 10 (1998)
Issue (Month): 3 ()
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- Mariolis, Theodore & Tsoulfidis, Lefteris, 2012. "On Bródy’s conjecture: facts and figures from the US economy," MPRA Paper 43719, University Library of Munich, Germany.
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- Christian Bidard & Tom Schatteman, 2001. "The Spectrum of Random Matrices," Economic Systems Research, Taylor and Francis Journals, vol. 13(3), pages 289-298.
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