116 citations · 1.1k across the 72 of their papers we have counts for
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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…