On Hypothesis about the Second Eigenvalue of the Leontief Matrix

Stanisław Białas and Henryk Gurgul

Economic Systems Research, 1998, vol. 10, issue 3, 285-290

Abstract: 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.

Keywords: Equilibrium; second eigenvalue; convergence (search for similar items in EconPapers)
Date: 1998
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/762947113 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:ecsysr:v:10:y:1998:i:3:p:285-290

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/CESR20

DOI: 10.1080/762947113

Access Statistics for this article

Economic Systems Research is currently edited by Bart Los and Manfred Lenzen

More articles in Economic Systems Research from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().