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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Lax conjecture is true


Authors: A. S. Lewis, P. A. Parrilo and M. V. Ramana
Journal: Proc. Amer. Math. Soc. 133 (2005), 2495-2499
MSC (2000): Primary 15A45, 90C25, 52A41
Published electronically: March 31, 2005
MathSciNet review: 2146191
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07752-X
PII: S 0002-9939(05)07752-X
Keywords: Hyperbolic polynomial, Lax conjecture, hyperbolicity cone, semidefinite representable
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
Article copyright: © Copyright 2005 American Mathematical Society