The Lax Conjecture Is True

  title={The Lax Conjecture Is True},
  author={Seth Lewis and Pablo A. Parrilo and Motakuri V. Ramana},
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. Consider a polynomial p on R of degree d (the maximum of the degrees of the monomials in the expansion of p). We call p homogeneous if p(tw) = tp(w) for all real t and vectors w ∈ R: equivalently, every monomial in the expansion of p has degree d. We denote the set of such… CONTINUE READING
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