On the Existence of Schur-like Forms for Matrices with Symmetry Structures

dc.contributor.authorMehl, Christian
dc.date.accessioned2023-07-17T14:51:48Z
dc.date.available2023-07-17T14:51:48Z
dc.date.issued2020-03-13
dc.date.updated2023-06-15T14:28:44Z
dc.description.abstractSchur-like forms are developed for matrices that have a symmetry structure with respect to an indefinite inner product induced by a Hermitian and unitary Gram matrix. It is characterized under which conditions these forms can be computed by structure-preserving unitary transformations. The main results combines and generalizes the two well-known results from the literature that on the one hand any normal matrix can be unitarily diagonalized and on the other hand a Hamiltonian matrix can be transformed to Hamiltonian Schur form via a unitary similarity transformation if and only if its purely imaginary eigenvalues satisfy certain conditions that involve the sign characteristic of the matrix under consideration.en
dc.identifier.eissn2305-2228
dc.identifier.issn2305-221X
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/19315
dc.identifier.urihttps://doi.org/10.14279/depositonce-18111
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.subject.otherindefinite inner producten
dc.subject.otherSchur-like formen
dc.subject.otherHamiltonian matrixen
dc.subject.otherpolynomially H-normal matrixen
dc.subject.other65F15en
dc.subject.other15A21en
dc.subject.other15A63en
dc.titleOn the Existence of Schur-like Forms for Matrices with Symmetry Structuresen
dc.typeArticle
dc.type.versionpublishedVersion
dcterms.bibliographicCitation.doi10.1007/s10013-020-00394-3
dcterms.bibliographicCitation.issue4
dcterms.bibliographicCitation.journaltitleVietnam Journal of Mathematics
dcterms.bibliographicCitation.originalpublishernameSpringer
dcterms.bibliographicCitation.originalpublisherplaceHeidelberg
dcterms.bibliographicCitation.pageend845
dcterms.bibliographicCitation.pagestart831
dcterms.bibliographicCitation.volume48
dcterms.rightsHolder.referenceCreative-Commons-Lizenz
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Mathematik
tub.publisher.universityorinstitutionTechnische Universität Berlin

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