Real algebraic geometry for matrices over commutative rings

DOI10.1016/j.jalgebra.2012.03.011zbMath1256.13016arXiv1106.5239OpenAlexW2077300652MaRDI QIDQ1758260

Jakob Cimprič

Publication date: 8 November 2012

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5239

zbMATH Keywords

matrix polynomialsPositivstellensatzpreorderingsum of squarespositive polynomials

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Semialgebraic sets and related spaces (14P10) Real algebra (13J30)

Related Items (11)

Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets ⋮ Symmetry reduction of states. II: A non-commutative positivstellensatz for \(\mathbb{C} \mathbb{P}^n\) ⋮ Simultaneous Diagonalization via Congruence of Hermitian Matrices: Some Equivalent Conditions and a Numerical Solution ⋮ A real nullstellensatz for free modules ⋮ Finsler's lemma for matrix polynomials ⋮ Some positivstellensätze for polynomial matrices ⋮ A note on nondegenerate matrix polynomials ⋮ Handelman's Positivstellensatz for polynomial matrices positive definite on polyhedra ⋮ Positive univariate trace polynomials ⋮ A Matrix Positivstellensatz with Lifting Polynomials ⋮ Positivstellensätze for polynomial matrices

Cites Work

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• Strict positivstellensätze for matrix polynomials with scalar constraints
• A non-commutative real Nullstellensatz and Hilbert's 17th problem
• Anneaux preordonnes
• A Nullstellensatz and a Positivstellensatz in semialgebraic geometry
• Non-commutative Real Algebraic Geometry - Some Basic Concepts and First Ideas
• Formally Real Involutions on Central Simple Algebras
• On the absence of uniform denominators in Hilbert’s 17th problem

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