IDEAS home Printed from https://ideas.repec.org/a/taf/ecsysr/v10y1998i3p285-290.html
   My bibliography  Save this article

On Hypothesis about the Second Eigenvalue of the Leontief Matrix

Author

Listed:
  • Stanisław Białas
  • Henryk Gurgul

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.

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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/762947113
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/762947113?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    3. Anwar Shaikh & Luiza Nassif, 2018. "Eigenvalue distribution, matrix size and the linearity of wage-profit curves," Working Papers 1812, New School for Social Research, Department of Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:ecsysr:v:10:y:1998:i:3:p:285-290. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CESR20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.