Jurij Volčič

activity

20152026

most citedGeometry of free loci and factorization of noncommutative polynomials

28 citations · 197 across the 30 of their papers we have counts for

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Showing 2015Show all

4 papers · 1 filter

math.RA2015★ 17 cited

Free loci of matrix pencils and domains of noncommutative rational functions

Igor Klep, Jurij Volčič

Consider a monic linear pencil $L (x) = I - A_{1} x_{1} - \dots - A_{g} x_{g}$ whose coefficients $A_{j}$ are $d \times d$ matrices. It is naturally evaluated at $g$ -tuples of matrices $X$ usi…

math.RA2015★ 1 cited

Multipartite rational functions

Igor Klep, Victor Vinnikov, Jurij Volčič

Consider a tensor product of free algebras over a field $k$ , the so-called multipartite free algebra $A = k ⟨ X^{(1)} ⟩ \otimes \dots \otimes k ⟨ X^{(G)} ⟩$ . It is…

math.RA2015

Matrix coefficient realization theory of noncommutative rational functions

Jurij Volčič

Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressi…

math.RA2015★ 9 cited

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…