VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • On trace-convex noncommutative polynomials
    Klep, Igor, matematik ; McCullough, Scott ; Nelson, Christopher
    To each continuous function ▫$f: \mathbb{R} \to \mathbb{R}$▫ there is an associated trace function on ▫$n \times n$▫ real symmetric matrices ▫$\mathrm{Tr}f$▫. The classical Klein lemma states that ... ▫$f$▫ is convex if and only if ▫$\mathrm{Tr}f$▫ is convex. In this note we present an algebraic strengthening of this lemma for univariate polynomials ▫$f: \mathrm{Tr}f$▫ is convex if and only if the noncommutative second directional derivative of ▫$f$▫ is a sum of Hermitian squares and commutators in a free algebra. We also give a localized version of this result.
    Vir: Michigan mathematical journal. - ISSN 0026-2285 (Vol. 65, iss. 1, 2016, str. 131-146)
    Vrsta gradiva - članek, sestavni del
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 17668185

vir: Michigan mathematical journal. - ISSN 0026-2285 (Vol. 65, iss. 1, 2016, str. 131-146)
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