This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Helton, J. WilliamKlep, IgorVolčič, Jurij2017-11-232019-06-2820171864-7596https://doi.org/10.34657/2426https://oa.tib.eu/renate/handle/123456789/2613The free singularity locus of a noncommutative polynomial f is defined to be the sequence Zn(f)={X∈Mgn:detf(X)=0} of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if Zn(f) is eventually irreducible. A key step in the proof is an irreducibility result for linear pencils. Apart from its consequences to factorization in a free algebra, the paper also discusses its applications to invariant subspaces in perturbation theory and linear matrix inequalities in real algebraic geometry.application/pdfeng510Noncommutative polynomialfactorizationsingularity locuslinear matrix inequalityspectrahedronreal algebraic geometryrealizationfree algebrainvariant theoryReport