Strict Positivstellensätze for matrix polynomials with scalar constraints

Details Strict Positivstellensätze for matrix polynomials with scalar constraints Strict Positivstellensätze for matrix polynomials with scalar constraints

2010-11-22

arxiv.org/abs/1011.4930v2

Mathematics

Algebraic Geometry

6 pages, to appear in Linear Algebra and its Applications

Scientific paper

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.

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