Sign characteristics of regular Hermitian matrix pencils under generic rank-1 and rank-2 perturbations

dc.contributor.authorBatzke, Leonhard
dc.date.accessioned2021-12-17T10:11:59Z
dc.date.available2021-12-17T10:11:59Z
dc.date.issued2014-11-24
dc.description.abstractThe spectral behavior of regular Hermitian matrix pencils is examined under certain structure-preserving rank-1 and rank-2 perturbations. Since Hermitian pencils have signs attached to real (and infinite) blocks in canonical form, it is not only the Jordan structure but also this so-called sign characteristic that needs to be examined under perturbation. The observed effects are as follows: Under a rank-1 or rank-2 perturbation, generically the largest one or two, respectively, Jordan blocks at each eigenvalue λ are destroyed, and if λ is an eigenvalue of the perturbation, also one new block of size one is created at λ. If λ is real (or infinite), additionally all signs at λ but one or two, respectively, that correspond to the destroyed blocks, are preserved under perturbation. Also, if the potential new block of size one is real, its sign is in most cases prescribed to be the sign that is attached to the eigenvalue λ in the perturbation.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15800
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14573
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.othermatrix pencilen
dc.subject.otherHermitian matrix pencilen
dc.subject.othersign characteristicen
dc.subject.otherrank one perturbationen
dc.subject.otherrank two perturbationen
dc.subject.othergeneric perturbationen
dc.titleSign characteristics of regular Hermitian matrix pencils under generic rank-1 and rank-2 perturbationsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2014, 36en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200015A22 Matrix pencilsen
tub.subject.msc200047A55 Perturbation theoryen

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