(Hessenberg) eigenvalue-eigenmatrix relations
| Autor: | Zemke, Jens-Peter M. |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2004 |
| Předmět: |
15A15
15A18 eigenvalue-eigenmatrix relations Eigenwertberechnung Determinants permanents other special matrix functions [15A15] Matrix equations and identities [15A24] Algebraic eigenvalue problem 15A57 15A24 Eigenvalues singular values and eigenvectors [15A18] adjugate Jordan normal form ddc:510 principal submatrices Mathematik [510] Matrizen-Eigenwertaufgabe Other types of matrices (Hermitian skew-Hermitian etc.) [15A57] |
| Zdroj: | Preprint. Published in: Linear Algebra and its ApplicationsVolume 414, Issues 2–3, 15 April 2006, Pages 589-606 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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