On the Choi-Lam analogue of Hilbert's 1888 theorem for symmetric forms

Charu Goel, Salma Kuhlmann, Bruce Reznick

Research output: Contribution to journalArticle

Abstract

A famous theorem of Hilbert from 1888 states that for given n and d, every positive semidefinite (psd) real form of degree 2d in n variables is a sum of squares (sos) of real forms if and only if n=2 or d=1 or (n,2d)=(3,4). In 1976, Choi and Lam proved the analogue of Hilbert's Theorem for symmetric forms by assuming the existence of psd not sos symmetric n-ary quartics for n≥5. In this paper we complete their proof by constructing explicit psd not sos symmetric n-ary quartics for n≥5.

Original languageEnglish (US)
Pages (from-to)114-120
Number of pages7
JournalLinear Algebra and Its Applications
Volume496
DOIs
StatePublished - May 1 2016

Keywords

  • Positive polynomials
  • Sums of squares
  • Symmetric forms

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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