74 citations · 668 across the 48 of their papers we have counts for
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Factorization of noncommutative polynomials and Nullstellensätze for the free algebra
J. William Helton, Igor Klep, Jurij Volčič
This article gives a class of Nullstellensätze for noncommutative polynomials. The singularity set of a noncommutative polynomial is , where $…
Geometry of free loci and factorization of noncommutative polynomials
J. William Helton, Igor Klep, Jurij Volčič
The free singularity locus of a noncommutative polynomial f is defined to be the sequence of hypersurfaces. The main theorem of this article s…
Non-Commutative Representations of Families of k^2 Commutative Polynomials in 2k^2 Commuting Variables
Harry Dym, J. W. Helton, Caleb Meier
Given a collection P of k^2 commutative polynomials in 2k^2 commutative variables, the objective is to find a condensed representation of these polynomials in terms of a single non…
On real one-sided ideals in a free algebra
Jakob Cimprič, J. William Helton, Igor Klep +2
In classical and real algebraic geometry there are several notions of the radical of an ideal I. There is the vanishing radical defined as the set of all real polynomials vanishing…
The convex Positivstellensatz in a free algebra
J. William Helton, Igor Klep, Scott McCullough
Given a monic linear pencil L in g variables let D_L be its positivity domain, i.e., the set of all g-tuples X of symmetric matrices of all sizes making L(X) positive semidefinite.…
Determinant Expansions of Signed Matrices and of Certain Jacobians
J. William Helton, Igor Klep, Raul Gomez
This paper treats two topics: matrices with sign patterns and Jacobians of certain mappings. The main topic is counting the number of plus and minus coefficients in the determinant…