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Noncommutative convexity arises from linear matrix inequalities |
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| Authors: | J. William Helton Victor Vinnikov |
| Affiliation: | a Mathematics Department, University of California at San Diego, CA 92093, USA b Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA c Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva, Israel |
| Abstract: | This paper concerns polynomials in g noncommutative variables x=(x1,…,xg), inverses of such polynomials, and more generally noncommutative “rational expressions” with real coefficients which are formally symmetric and “analytic near 0.” The focus is on rational expressions r=r(x) which are “matrix convex” near 0; i.e., those rational expressions r for which there is an ?>0 such that if X=(X1,…,Xg) is a g-tuple of n×n symmetric matrices satisfying |
| Keywords: | Noncommutative (NC) rational functions Matrix convexity Noncommutative convexity Linear matrix inequalities Matrix inequalities Determinantal representations Noncommutative realizations |
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