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dc.contributor.authorHelton, J. William
dc.contributor.authorKlep, Igor
dc.contributor.authorVolčič, Jurij
dc.contributor.authorHelton, J. William
dc.date.accessioned2017-11-06T11:08:24Z
dc.date.available2017-11-06T11:08:24Z
dc.date.issued2017-10-02
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1322
dc.descriptionMSC 2010: 13J30; 15A22; 47A56 (Primary) | 14P10; 16U30; 16R30 (Secondary)en_US
dc.descriptionResearch in Pairs 2017en_US
dc.description.abstractThe free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if $Z_n(f)$ 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.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2017,23
dc.subjectNoncommutative Polynomialen_US
dc.subjectFactorizationen_US
dc.subjectSingularity locusen_US
dc.subjectLinear matrix inequalityen_US
dc.subjectSpectrahedronen_US
dc.subjectReal algebraic geometryen_US
dc.subjectRealizationen_US
dc.subjectFree algebraen_US
dc.subjectInvariant theoryen_US
dc.titleGeometry of Free Loci and Factorization of Noncommutative Polynomialsen_US
dc.typePreprinten_US
dc.rights.licenseDieses 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.de
dc.rights.licenseThis 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.en
dc.identifier.doi10.14760/OWP-2017-23
local.scientificprogramResearch in Pairs 2017en_US
local.series.idOWP-2017-23
local.subject.msc13
local.subject.msc15
local.subject.msc47
local.subject.msc14
local.subject.msc16
dc.identifier.urnurn:nbn:de:101:1-2017110614174
dc.identifier.ppn165677299X


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