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.accessioned2021-12-17T10:12:56Z
dc.date.available2021-12-17T10:12:56Z
dc.date.issued2015-12-04
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.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15831
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14604
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
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.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.issuenumber2015, 32en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200015A57 Other types of matricesen
tub.subject.msc200065F15 Eigenvalues, eigenvectorsen
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