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(Hessenberg) eigenvalue-eigenmatrix relations
Citation Link: https://doi.org/10.15480/882.99
Publikationstyp
Preprint
Date Issued
2004-09
Sprache
English
Author(s)
Institut
TORE-DOI
First published in
Preprints des Institutes für Mathematik;Bericht 78
Number in series
78
Citation
Preprint. Published in: Linear Algebra and its ApplicationsVolume 414, Issues 2–3, 15 April 2006, Pages 589-606
Publisher DOI
Scopus ID
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.
Subjects
Algebraic eigenvalue problem
eigenvalue-eigenmatrix relations
Jordan normal form
adjugate
principal submatrices
DDC Class
510: Mathematik
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