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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.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


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