Determinantal representations and the Hermite matrix

DOI10.1307/mmj/1370870379zbMath1273.15005arXiv1108.4380OpenAlexW2161422332WikidataQ61677668 ScholiaQ61677668MaRDI QIDQ357531

Tim Netzer, Daniel Plaumann, Andreas Thom

Publication date: 30 July 2013

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.4380

zbMATH Keywords

determinantal representationHermite matricesreal-zero polynomialssum-of-squares representation

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (15)

A note on the hyperbolicity cone of the specialized Vámos polynomial ⋮ Symmetric determinantal representations in characteristic 2 ⋮ Testing hyperbolicity of real polynomials ⋮ A complete characterization of determinantal quadratic polynomials ⋮ Determinantal representations and Bézoutians ⋮ Robust domain of attraction estimation for a tumor growth model ⋮ Stable and real-zero polynomials in two variables ⋮ The Chow form of a reciprocal linear space ⋮ Burnside graphs, algebras generated by sets of matrices, and the Kippenhahn conjecture ⋮ Certifying Polynomial Nonnegativity via Hyperbolic Optimization ⋮ Hyperbolic polynomials and generalized Clifford algebras ⋮ Hyperbolic polynomials, interlacers, and sums of squares ⋮ Examples for the quantum Kippenhahn theorem ⋮ LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future ⋮ Determinantal Representations of Stable Polynomials

Cites Work

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• Symmetric determinantal representation of polynomials
• Polynomials with and without determinantal representations
• Obstructions to determinantal representability
• Detecting rigid convexity of bivariate polynomials
• Noncommutative convexity arises from linear matrix inequalities
• Complete description of determinantal representations of smooth irreducible curves
• Positive symmetric functions
• Linear matrix inequality representation of sets
• Newton's Identities
• A Note on Hyperbolic Polynomials.
• Algorithms in real algebraic geometry

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