Free convex sets defined by rational expressions have LMI representations

zbMath1298.47025arXiv1209.3412MaRDI QIDQ5168611

J. William Helton, Scott A. McCullough

Publication date: 18 July 2014

Full work available at URL: https://arxiv.org/abs/1209.3412

zbMATH Keywords

linear matrix inequalityfree convexitymatrix convexitynoncommutative rational functionfree rational function

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Semialgebraic sets and related spaces (14P10) Convex sets and cones of operators (47L07)

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Non‐commutative manifolds, the free square root and symmetric functions in two non‐commuting variables ⋮ Plurisubharmonic noncommutative rational functions ⋮ Empirical Properties of Optima in Free Semidefinite Programs ⋮ Noncommutative rational Clark measures ⋮ On domains of noncommutative rational functions ⋮ Bianalytic free maps between spectrahedra and spectraballs ⋮ Quadratic modules, 𝐶*-algebras, and free convexity ⋮ Realizations of non-commutative rational functions around a matrix centre. II: The lost-abbey conditions

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