On the sign characteristics of Hermitian matrix polynomials

dc.contributor.authorMehrmann, Volker
dc.contributor.authorNoferini, Vanni
dc.contributor.authorTisseur, Françoise
dc.contributor.authorXu, Hongguo
dc.date.accessioned2019-11-14T16:42:26Z
dc.date.available2019-11-14T16:42:26Z
dc.date.issued2016-09-14
dc.description.abstractThe sign characteristics of Hermitian matrix polynomials are discussed, and in particular an appropriate definition of the sign characteristics associated with the eigenvalue infinity. The concept of sign characteristic arises in different forms in many scientific fields, and is essential for the stability analysis in Hamiltonian systems or the perturbation behavior of eigenvalues under structured perturbations. We extend classical results by Gohberg, Lancaster, and Rodman to the case of infinite eigenvalues. We derive a systematic approach, studying how sign characteristics behave after an analytic change of variables, including the important special case of Möbius transformations, and we prove a signature constraint theorem. We also show that the sign characteristic at infinity stays invariant in a neighborhood under perturbations for even degree Hermitian matrix polynomials, while it may change for odd degree matrix polynomials. We argue that the non-uniformity can be resolved by introducing an extra zero leading matrix coefficient.en
dc.description.sponsorshipEC/FP7/EU/267526/Functions of Matrices: Theory and Computation/MATFUNen
dc.description.sponsorshipDFG, 5485610, FZT 86: Matheon - Mathematik für Schlüsseltechnologien: Modellierung, Simulation und Optimierung realer Prozesseen
dc.identifier.eissn1873-1856
dc.identifier.issn0024-3795
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/10313
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-9275
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510 Mathematikde
dc.subject.otherhermitian matrix polynomialen
dc.subject.othersign characteristicen
dc.subject.othersign characteristic at infinityen
dc.subject.othersign featureen
dc.subject.othersignature constrainten
dc.subject.otherperturbation theoryen
dc.titleOn the sign characteristics of Hermitian matrix polynomialsen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1016/j.laa.2016.09.002
dcterms.bibliographicCitation.journaltitleLinear Algebra and its Applicationsen
dcterms.bibliographicCitation.originalpublishernameElsevieren
dcterms.bibliographicCitation.originalpublisherplaceAmsterdamen
dcterms.bibliographicCitation.pageend364
dcterms.bibliographicCitation.pagestart328
dcterms.bibliographicCitation.volume511
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Numerische Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Mathematikde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinde
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