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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Lax conjecture is true
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by A. S. Lewis, P. A. Parrilo and M. V. Ramana PDF
Proc. Amer. Math. Soc. 133 (2005), 2495-2499 Request permission

Abstract:

In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov.
References
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Additional Information
  • A. S. Lewis
  • Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
  • Address at time of publication: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853
  • Email: aslewis@sfu.ca, aslewis@orie.cornell.edu
  • P. A. Parrilo
  • Affiliation: Automatic Control Laboratory, Swiss Federal Institute of Technology, CH-8092 Zürich, Switzerland
  • Email: parrilo@control.ee.ethz.ch
  • M. V. Ramana
  • Affiliation: Corporate Research and Development, United Airlines Inc., Elk Grove Village, Illinois 60007
  • Email: motakuri_ramana@yahoo.com
  • Received by editor(s): April 2, 2003
  • Published electronically: March 31, 2005
  • Additional Notes: The research of the first author was supported by NSERC
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2495-2499
  • MSC (2000): Primary 15A45, 90C25, 52A41
  • DOI: https://doi.org/10.1090/S0002-9939-05-07752-X
  • MathSciNet review: 2146191