On domains of noncommutative rational functions

Jurij Volčič

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities theorem of Kalyuzhnyi-Verbovetskyi and Vinnikov. Furthermore, for noncommutative rational functions which are regular at a scalar point it is proved that their domains and stable extended domains coincide.

Original languageEnglish
Pages (from-to)69-81
Number of pages13
JournalLinear Algebra and Its Applications
StatePublished - 1 Mar 2017
Externally publishedYes


  • Extended domain
  • Free function theory
  • Minimal realization
  • Noncommutative rational function
  • Singularities

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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