VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Finsler's Lemma for matrix polynomials
    Cimprič, Jaka
    Finsler's Lemma charactrizes all pairs of symmetric ▫$n \times n$▫ real matrices ▫$A$▫ and ▫$B$▫ which satisfy the property that ▫$v^T A v > 0$▫ for every nonzero ▫$v \in \mathbb{R}^n$▫ such that ... ▫$v^T B v = 0$▫. We extend this characterization to all symmetric matrices of real multivariate polynomials, but we need an additional assumption that ▫$B$▫ is negative semidefinite outside some ball. We also give two applications of this result to Noncommutative Real Algebraic Geometry which for ▫$n=1$▫ reduce to the usual characterizations of positive polynomials on varieties and on compact sets.
    Vir: Linear algebra and its applications. - ISSN 0024-3795 (Vol. 465, 2015, str. 239-261)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2015
    Jezik - angleški
    COBISS.SI-ID - 17193817

    Povezava(-e):

    http://dx.doi.org/10.1016/j.laa.2014.09.037

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