Analytic Results for the Eigenvalues of Certain Tridiagonal Matrices

Analytic Results for the Eigenvalues of Certain Tridiagonal Matrices

The eigenvalue problem for a certain tridiagonal matrix with complex coefficients is considered. The eigenvalues and eigenvectors are shown to be expressible in terms of solutions of a certain scalar trigonometric equation. Explicit solutions of this equation are obtained for several special cases,...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2008-01, Vol.30 (2), p.639-656
1. Verfasser: Willms, Allan R.
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Eigenvectors
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Beschreibung
Zusammenfassung:The eigenvalue problem for a certain tridiagonal matrix with complex coefficients is considered. The eigenvalues and eigenvectors are shown to be expressible in terms of solutions of a certain scalar trigonometric equation. Explicit solutions of this equation are obtained for several special cases, and further analysis of this equation in several other cases provides information about the distribution of eigenvalues.
ISSN:0895-4798
1095-7162
DOI:10.1137/070695411