Extreme points of matrix convex sets, free spectrahedra, and dilation theory
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Publication:1651373
DOI10.1007/s12220-017-9866-4OpenAlexW3106198068MaRDI QIDQ1651373
Eric Evert, J. William Helton, Igor Klep, Scott A. McCullough
Publication date: 12 July 2018
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.00025
extreme pointsemialgebraic setdilation theorylinear matrix inequality (LMI)spectrahedronfree real algebraic geometrymatrix convex set
Semidefinite programming (90C22) Operator spaces and completely bounded maps (46L07) Convex sets and cones of operators (47L07) Real algebra (13J30)
Related Items (17)
Passive linear continuous-time systems: characterization through structure ⋮ Geometry of free loci and factorization of noncommutative polynomials ⋮ Facial structure of matrix convex sets ⋮ Complex free spectrahedra, absolute extreme points, and dilations ⋮ Empirical Properties of Optima in Free Semidefinite Programs ⋮ Optimal arrangements of classical and quantum states with limited purity ⋮ Polytope compatibility—From quantum measurements to magic squares ⋮ Spectrahedral Containment and Operator Systems with Finite-Dimensional Realization ⋮ Compressions of compact tuples ⋮ Dilation theory: a guided tour ⋮ An introduction to matrix convex sets and free spectrahedra ⋮ Passive linear discrete-time systems: characterization through structure ⋮ Universality of Weyl unitaries ⋮ Shape, scale, and minimality of matrix ranges ⋮ Dilation theory in finite dimensions and matrix convexity ⋮ Arveson extreme points span free spectrahedra ⋮ The Arveson boundary of a free quadrilateral is given by a noncommutative variety
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