116 citations · 1.1k across the 72 of their papers we have counts for
21 papers · 1 filter
Ranks of linear matrix pencils separate simultaneous similarity orbits
Harm Derksen, Igor Klep, Visu Makam +1
This paper solves the two-sided version and provides a counterexample to the general version of the 2003 conjecture by Hadwin and Larson. Consider evaluations of linear matrix penc…
Positive univariate trace polynomials
Igor Klep, James Eldred Pascoe, Jurij Volčič
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols a…
Noncommutative rational functions invariant under the action of a finite solvable group
Igor Klep, James Eldred Pascoe, Gregor Podlogar +1
This paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in generators. These invariant skew fields are alwa…
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 $…
Local theory of free noncommutative functions: germs, meromorphic functions and Hermite interpolation
Igor Klep, Victor Vinnikov, Jurij Volčič
Free analysis is a quantization of the usual function theory much like operator space theory is a quantization of classical functional analysis. Basic objects of free analysis are…
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…
Skolem-Noether algebras
Matej Brešar, Christoph Hanselka, Igor Klep +1
An algebra is called a Skolem-Noether algebra (SN algebra for short) if for every central simple algebra , every homomorphism extends to an inner automorph…
Positive trace polynomials and the universal Procesi-Schacher conjecture
Igor Klep, Špela Špenko, Jurij Volčič
Positivstellensatz is a fundamental result in real algebraic geometry providing algebraic certificates for positivity of polynomials on semialgebraic sets. In this article Positivs…
Regular and positive noncommutative rational functions
Igor Klep, James Eldred Pascoe, Jurij Volčič
Call a noncommutative rational function regular if it has no singularities, i.e., is defined for all tuples of self-adjoint matrices . In this article regular noncomm…
Free loci of matrix pencils and domains of noncommutative rational functions
Igor Klep, Jurij Volčič
Consider a monic linear pencil whose coefficients are matrices. It is naturally evaluated at -tuples of matrices usi…
Multipartite rational functions
Igor Klep, Victor Vinnikov, Jurij Volčič
Consider a tensor product of free algebras over a field , the so-called multipartite free algebra . It is…
Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three
Kenneth J. Dykema, Igor Klep
Given a positive integer d, the Kaplansky-Lvov conjecture states that the set of values of a multilinear noncommutative polynomial f on the matrix algebra M_d(C) is a vector subspa…
Sweeping words and the length of a generic vector subspace of M_n(F)
Igor Klep, Špela Špenko
The main result of this short note is a generic version of Paz's conjecture on the lengths of generating sets in matrix algebras. Consider a generic g-tuple A=(A_1,..., A_g) of nxn…
Null- and Positivstellensätze for rationally resolvable ideals
Igor Klep, Victor Vinnikov, Jurij Volčič
Hilbert's Nullstellensatz characterizes polynomials that vanish on the vanishing set of an ideal in C[x]. In the free algebra C<X> the vanishing set of a two-sided ideal I is defin…
Free function theory through matrix invariants
Igor Klep, Špela Špenko
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommut…
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…
A local-global principle for linear dependence of noncommutative polynomials
Matej Bresar, Igor Klep
A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino…
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.…
Values of Noncommutative Polynomials, Lie Skew-Ideals and the Tracial Nullstellensatz
Matej Bresar, Igor Klep
A subspace of an algebra with involution is called a Lie skew-ideal if it is closed under Lie products with skew-symmetric elements. Lie skew-ideals are classified in central simpl…
The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution
Igor Klep, Thomas Unger
In 1976 Procesi and Schacher developed an Artin-Schreier type theory for central simple algebras with involution and conjectured that in such an algebra a totally positive element…
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…