Noncommutative Convexity Arises from Linear Matrix Inequalities. J. William Helton, Scott A. Mccullough, and Victor Vinnikov

@inproceedings{HeltonNoncommutativeCA,
  title={Noncommutative Convexity Arises from Linear Matrix Inequalities. J. William Helton, Scott A. Mccullough, and Victor Vinnikov},
  author={J. William Helton and Scott A. McCullough and Victor Vinnikov}
}
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” on the unit ball; i.e., those rational expressions r such that if X = (X1, . . . , Xg) is a g-tuple of n × n symmetric matrices satisfying In − ( X 1 + · · · + X g ) is… CONTINUE READING
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