Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

DOI10.1090/memo/1232zbMath1447.47009arXiv1412.1481OpenAlexW2963150178MaRDI QIDQ5383906

J. William Helton, Igor Klep, Markus Schweighofer, Scott A. McCullough

Publication date: 20 June 2019

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

Full work available at URL: https://arxiv.org/abs/1412.1481

zbMATH Keywords

robust stabilitylinear matrix inequalitydilationbinomial distributioncompletely positive mapbeta distributionspectrahedronfree analysisfree spectrahedronmatrix cube problem

Mathematics Subject Classification ID

Semidefinite programming (90C22) Probability distributions: general theory (60E05) Gamma, beta and polygamma functions (33B15) Operator spaces and completely bounded maps (46L07) Dilations, extensions, compressions of linear operators (47A20) Research exposition (monographs, survey articles) pertaining to operator theory (47-02)

Related Items (20)

Noncommutative Choquet simplices ⋮ A tensor norm approach to quantum compatibility ⋮ Density of rational points near/on compact manifolds with certain curvature conditions ⋮ Extreme points of matrix convex sets, free spectrahedra, and dilation theory ⋮ Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms ⋮ Plurisubharmonic noncommutative rational functions ⋮ Noncommutative rational Clark measures ⋮ Polytope compatibility—From quantum measurements to magic squares ⋮ Bilinear matrix inequalities and polynomials in several freely noncommuting variables ⋮ Compatibility of Quantum Measurements and Inclusion Constants for the Matrix Jewel ⋮ Classifying linear matrix inequalities via abstract operator systems ⋮ Spectrahedral Containment and Operator Systems with Finite-Dimensional Realization ⋮ Complete order equivalence of spin unitaries ⋮ Dilation theory: a guided tour ⋮ An introduction to matrix convex sets and free spectrahedra ⋮ Noncommutative polynomials describing convex sets ⋮ Bianalytic free maps between spectrahedra and spectraballs ⋮ Shape, scale, and minimality of matrix ranges ⋮ Non-commutative rational functions in the full Fock space ⋮ Dilations of unitary tuples

Cites Work

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• Matrix positivity preservers in fixed dimension. I
• Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets
• The convex Positivstellensatz in a free algebra
• Every convex free basic semi-algebraic set has an LMI representation
• Multidimensional circuit synthesis and multivariable dilation theory
• Matrix convexity: Operator analogues of the bipolar and Hahn-Banach theorems
• A general framwork for a multi-operator functional calculus
• The Choquet boundary of an operator system
• Bounds for the difference between median and mean of beta and negative binomial distributions
• Interpolation of rational matrix functions
• Metric constrained interpolation, commutant lifting and systems
• Closed form summation for classical distributions: variations on a theme of de Moivre
• Quotients, exactness, and nuclearity in the operator system category
• The matricial relaxation of a linear matrix inequality
• Subalgebras of \(C^ *\)-algebras
• Subalgebras of C\(^*\)-algebras. II
• The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra
• Harmonic analysis of operators on Hilbert space
• Generalization of Simmons' theorem
• On Tractable Approximations of Uncertain Linear Matrix Inequalities Affected by Interval Uncertainty
• Containment Problems for Polytopes and Spectrahedra
• Operator-Valued Measures, Dilations, and the Theory of Frames
• Foundations of Free Noncommutative Function Theory
• Dilations of frames, operator valued measures and bounded linear maps
• The noncommutative Choquet boundary
• The mathematical legacy of William Arveson
• Linear matrix inequality representation of sets
• Free analysis questions II: The Grassmannian completion and the series expansions at the origin
• Linear Matrix Inequalities in System and Control Theory
• Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
• Semidefinite relaxation and nonconvex quadratic optimization
• Dilations, Inclusions of Matrix Convex Sets, and Completely Positive Maps
• Semidefinite Optimization and Convex Algebraic Geometry
• Operator system quotients of matrix algebras and their tensor products
• Framings and dilations
• Analytic Inequalities
• Functions of several noncommuting variables
• REPRESENTATIONS OF THE ANTICOMMUTATION RELATIONS
• Positive Functions on C ∗ -Algebras
• Handbook of semidefinite programming. Theory, algorithms, and applications

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