The Lax conjecture is true
arXiv:math/0304104 · doi:10.1090/S0002-9939-05-07752-X
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.
7 pages, Proceedings to the AMS, to appear. Added background material
Cited by in corpus (22)
- Polynomials with the half-plane property and matroid theory
- Obstructions to determinantal representability
- Determinantal representations of hyperbolic plane curves: An elementary approach
- Semidefinite Representation of the -Ellipse
- Computing Linear Matrix Representations of Helton-Vinnikov Curves
- Geometry of free loci and factorization of noncommutative polynomials
- The central curve in linear programming
- Livsic-type Determinantal Representations and Hyperbolicity
- Real Fibered Morphisms and Ulrich Sheaves
- Polynomial-sized Semidefinite Representations of Derivative Relaxations of Spectrahedral Cones
- Hyperbolicity preservers and majorization
- Semidefinite programming in matrix unknowns which are dimension free
- Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix
- Determinantal representations of semi-hyperbolic polynomials
- Quantum compression relative to a set of measurements
- Noncommutative polynomials describing convex sets
- Discrete concavity and the half-plane property
- A spectrahedral representation of the first derivative relaxation of the positive semidefinite cone
- Representations of Lie Algebras by non-Skewselfadjoint Operators in Hilbert Space
- Hyperbolicity cones are amenable
- Nuij type pencils of hyperbolic polynomials
- Computing symmetric determinantal representations