IDEAS home Printed from https://ideas.repec.org/a/taf/ecsysr/v9y1997i3p253-258.html
   My bibliography  Save this article

The Second Eigenvalue of the Leontief Matrix

Author

Listed:
  • Andras Brody

Abstract

According to Frobenius, a positive matrix possesses a unique positive eigenvector which belongs to a positive eigenvalue. This eigenvalue is of the largest absolute magnitude and the matrix admits no other positive eigenvector. If an arbitrary positive vector is repeatedly premultiplied by such a matrix, then the result tends towards this positive eigenvector. It is the second largest eigenvalue that determines the speed of convergence. The estimate of the second eigenvalue of a purely random flow coefficient matrix shows that its expected absolute magnitude declines monotonically with the size of the matrix. Hence, the larger the system is the faster is the convergence. A prescribed exactness of the eigenvector (of equilibrium prices or quantities) will be reached after a few—perhaps just a couple of—iterations in a large system.

Suggested Citation

  • Andras Brody, 1997. "The Second Eigenvalue of the Leontief Matrix," Economic Systems Research, Taylor & Francis Journals, vol. 9(3), pages 253-258.
    • Handle: RePEc:taf:ecsysr:v:9:y:1997:i:3:p:253-258
    DOI: 10.1080/09535319700000018
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/09535319700000018
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/09535319700000018?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.

    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:9:y:1997:i:3:p:253-258. 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.