Verlagslink DOI: 10.1016/j.laa.2005.11.002
Titel: (Hessenberg) eigenvalue-eigenmatrix relations
Sprache: Englisch
Autor/Autorin: Zemke, Jens-Peter M.
Schlagwörter: Algebraic eigenvalue problem;eigenvalue-eigenmatrix relations;Jordan normal form;adjugate;principal submatrices
Erscheinungsdatum: 2004
Quellenangabe: Preprint. Published in: Linear Algebra and its Applications Volume 414, Issues 2–3, 15 April 2006, Pages 589-606
Serie/Report Nr.: Preprints des Institutes für Mathematik;Bericht 78
Zusammenfassung (englisch): Explicit 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.
URI: http://tubdok.tub.tuhh.de/handle/11420/101
URN: urn:nbn:de:gbv:830-opus-1577
DOI: 10.15480/882.99
Institut: Mathematik E-10
Mathematics E-10
Dokumenttyp: Preprint (Vorabdruck)
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