The Lax conjecture is true

A.S. Lewis (aslewissfu.ca)
P.A. Parrilo (parrilocontrol.ee.ethz.ch)
M.V. Ramana (motakuri_ramanayahoo.com)

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.

Keywords: hyperbolic polynomial, Lax conjecture, hyperbolicity cone, semidefinite representable

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Department of Mathematics, Simon Fraser University, Canada

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Entry Submitted: 04/18/2003
Entry Accepted: 04/18/2003
Entry Last Modified: 04/18/2003

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