Strict Positivstellens\"atze for matrix polynomials with scalar constraints
Algebraic Geometry
2013-01-07 v2 Optimization and Control
Abstract
We extend Krivine's strict positivstellensatz for usual (real multivariate) polynomials to symmetric matrix polynomials with scalar constraints. The proof is an elementary computation with Schur complements. Analogous extensions of Schm\" udgen's and Putinar's strict positivstellensatz were recently proved by Hol and Scherer using methods from optimization theory.
Keywords
Cite
@article{arxiv.1011.4930,
title = {Strict Positivstellens\"atze for matrix polynomials with scalar constraints},
author = {Jaka Cimpric},
journal= {arXiv preprint arXiv:1011.4930},
year = {2013}
}
Comments
6 pages, to appear in Linear Algebra and its Applications