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