3 citations · 7 across the 4 of their papers we have counts for
4 papers · 1 filter
Positive Ulrich Sheaves
Christoph Hanselka, Mario Kummer
We provide a criterion for a coherent sheaf to be an Ulrich sheaf in terms of a certain bilinear form on its global sections. When working over the real numbers we call it a positi…
Positive Semidefinite Univariate Matrix Polynomials
Christoph Hanselka, Rainer Sinn
We study sum-of-squares representations of symmetric univariate real matrix polynomials that are positive semidefinite along the real line. We give a new proof of the fact that eve…
Characteristic Polynomials of Symmetric Matrices over the Univariate Polynomial Ring
Christoph Hanselka
Viewing a bivariate polynomial f in R[x,t] as a family of univariate polynomials in t parametrized by real numbers x, we call f real rooted if this family consists of monic polynom…
Definite Determinantal Representations of Ternary Hyperbolic Forms
Christoph Hanselka
We give a new and completely algebraic proof of the Helton-Vinnikov Theorem stating that every hyperbolic polynomial in three variables admits a definite linear determinantal repre…