English

Determinantal Representations and B\'ezoutians

Algebraic Geometry 2016-06-30 v3 Optimization and Control

Abstract

We show that for every smooth hyperbolic polynomial h there is another hyperbolic polynomial q such that qh has a definite determinantal representation. This is proved by considering sum-of-squares decompositions of certain bilinear forms called B\'ezoutians. Besides commutative algebra, the proof relies on results from real algebraic geometry.

Keywords

Cite

@article{arxiv.1308.5560,
  title  = {Determinantal Representations and B\'ezoutians},
  author = {Mario Kummer},
  journal= {arXiv preprint arXiv:1308.5560},
  year   = {2016}
}

Comments

v2: differently organized

R2 v1 2026-06-22T01:14:58.387Z