Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.99
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dc.contributor.authorZemke, Jens-Peter M.-
dc.date.accessioned2006-02-01T12:06:35Zde_DE
dc.date.available2006-02-01T12:06:35Zde_DE
dc.date.issued2004-09-
dc.identifier.citationPreprint. Published in: Linear Algebra and its ApplicationsVolume 414, Issues 2–3, 15 April 2006, Pages 589-606de_DE
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/101-
dc.description.abstractExplicit relations between eigenvalues, eigenmatrix entries and matrix elements are derived. First, a general, theoretical result based on the Taylor expansion of the adjugate of zI - A on the one hand and explicit knowledge of the Jordan decomposition on the other hand is proven. This result forms the basis for several, more practical and enlightening results tailored to non-derogatory, diagonalizable and normal matrices, respectively. Finally, inherent properties of (upper) Hessenberg, resp. tridiagonal matrix structure are utilized to construct computable relations between eigenvalues, eigenvector components, eigenvalues of principal submatrices and products of lower diagonal elements.en
dc.language.isoende_DE
dc.relation.ispartofseriesPreprints des Institutes für Mathematik;Bericht 78-
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectAlgebraic eigenvalue problemde_DE
dc.subjecteigenvalue-eigenmatrix relationsde_DE
dc.subjectJordan normal formde_DE
dc.subjectadjugatede_DE
dc.subjectprincipal submatricesde_DE
dc.subject.ddc510: Mathematikde_DE
dc.title(Hessenberg) eigenvalue-eigenmatrix relationsde_DE
dc.typePreprintde_DE
dc.date.updated2006-02-09T14:55:47Zde_DE
dc.identifier.urnurn:nbn:de:gbv:830-opus-1577de_DE
dc.identifier.doi10.15480/882.99-
dc.type.dinipreprint-
dc.subject.gndEigenwertberechnungde
dc.subject.gndMatrizen-Eigenwertaufgabede
dc.subject.ddccode510-
dc.subject.msc15A57:Other types of matrices (Hermitian, skew-Hermitian, etc.)en
dc.subject.msc15A15:Determinants, permanents, other special matrix functionsen
dc.subject.msc15A24:Matrix equations and identitiesen
dc.subject.msc15A18:Eigenvalues, singular values, and eigenvectorsen
dc.subject.msccode15A18-
dc.subject.msccode15A57-
dc.subject.msccode15A15-
dc.subject.msccode15A24-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-opus-1577de_DE
tuhh.publikation.typreportde_DE
tuhh.opus.id157de_DE
tuhh.oai.showtruede_DE
dc.identifier.hdl11420/101-
tuhh.abstract.englishExplicit relations between eigenvalues, eigenmatrix entries and matrix elements are derived. First, a general, theoretical result based on the Taylor expansion of the adjugate of zI - A on the one hand and explicit knowledge of the Jordan decomposition on the other hand is proven. This result forms the basis for several, more practical and enlightening results tailored to non-derogatory, diagonalizable and normal matrices, respectively. Finally, inherent properties of (upper) Hessenberg, resp. tridiagonal matrix structure are utilized to construct computable relations between eigenvalues, eigenvector components, eigenvalues of principal submatrices and products of lower diagonal elements.de_DE
tuhh.publisher.doi10.1016/j.laa.2005.11.002-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.99-
tuhh.type.opusPreprint (Vorabdruck)-
tuhh.institute.germanMathematik E-10de
tuhh.institute.englishMathematics E-10en
tuhh.institute.id47de_DE
tuhh.type.id20de_DE
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tuhh.gvk.hasppnfalse-
tuhh.series.namePreprints des Institutes für Mathematik-
dc.type.driverpreprint-
dc.identifier.oclc930767804-
dc.type.casraiOther-
tuhh.relation.ispartofseriesPreprints des Institutes für Mathematikde_DE
tuhh.relation.ispartofseriesnumber78de_DE
item.creatorGNDZemke, Jens-Peter M.-
item.cerifentitytypePublications-
item.seriesrefPreprints des Institutes für Mathematik;78-
item.mappedtypePreprint-
item.openairecristypehttp://purl.org/coar/resource_type/c_816b-
item.tuhhseriesidPreprints des Institutes für Mathematik-
item.grantfulltextopen-
item.openairetypePreprint-
item.languageiso639-1en-
item.creatorOrcidZemke, Jens-Peter M.-
item.fulltextWith Fulltext-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-5748-8727-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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