An elementary and constructive solution to Hilbert’s 17th Problem for matrices

DOI10.1090/S0002-9939-07-09068-5zbMath1126.12001arXivmath/0610388MaRDI QIDQ5429425

Christopher J. Hillar, Jia-Wang Nie

Publication date: 30 November 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610388

zbMATH Keywords

Hilbert's 17th problemreal closed fieldpositive semidefinite matrixsum of squaresArtin's theorem

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Matrices over function rings in one or more variables (15A54) Canonical forms, reductions, classification (15A21) Real algebra (13J30)

Related Items (10)

Symmetry reduction of states. II: A non-commutative positivstellensatz for \(\mathbb{C} \mathbb{P}^n\) ⋮ Dehomogenization for completely positive tensors ⋮ Rational Generalized Nash Equilibrium Problems ⋮ Generalized truncated moment problems with unbounded sets ⋮ Sums of squares. II: Matrix functions ⋮ Polynomial Norms ⋮ Noncommutative Positivstellensätze for pairs representation-vector ⋮ Determinantal representations and Bézoutians ⋮ The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution. ⋮ Sums of squares over totally real fields are rational sums of squares

Cites Work

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• Positive semidefinite biquadratic forms
• A non-commutative real Nullstellensatz and Hilbert's 17th problem
• Characterization of a class of matrices as sums of squares
• Matrix Analysis
• Model Theory

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