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Von Neumann Model Solutions Are Generalized Eigensystems

  • Gerald L. Thompson
  • Roman L. Weil

Abstract

General relations between the von Neumann model and eigensystems are derived. Every solution to a von Neuman model implies a generalized eigenvalue problem, perhaps in several different ways. Previously discovered interconnections are shown to be special instances of the general result. Analogues of the Shapley-Snow-Kaplansky formulas for basic optimal solutions to the von Neumann model are derived. The results have mathematical and economic implications, but do not improve existing computational methods. The derived generalized eigensystem is related to a normal form in the literature of matrix algebra due to Gantmacher.

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Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • Gerald L. Thompson
    • 1
  • Roman L. Weil
    • 2
  1. 1.Grad. School of Industrial AdministrationCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Graduate School of BusinessUniversity of ChicagoChicagoUSA

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