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.
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