EIGENVALUES AND EIGENVECTORS OF TRIDIAGONAL MATRICES

By S. Kouachi. 2006

96 citations recorded by the source corpus.

This paper is continuation of previous work by the present author, where explicit formulas for the eigenvalues associated with several tridiagonal matrices were given. In this paper the associated eigenvectors are calculated explicitly. As a consequence, a result obtained by Wen- Chyuan Yueh and independently by S. Kouachi, concerning the eigenvalues and in particular the corresponding eigenvectors of tridiagonal matrices, is generalized. Expressions for the eigenvectors are obtained that differ completely from those obtained by Yueh. The techniques used herein are based on theory of recurrent sequences. The entries situated on each of the secondary diagonals are not necessary equal as was the case considered by Yueh. n−1 j=1 are two finite subsequences of the sequences {aj} ∞ j=1 and {cj} ∞=1 of the field of complex numbers C, respectively, and α, β and b are complex numbers. We suppose that

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6f102e06609643de90dd91922187aafddd217488

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In Mathematical Physics

1. Massimiliano Zingales
2. Mario Di Paola

Citations in the corpus

• A discrete mechanical model of fractional hereditary materials (2013, background): “The eigenvalues λj and the normalized eigenvectors φj of particular tridiagonal matrix A may be found in [22, 23] and they are reported below:”
• An explicit formula for eigenvalues of Bethe trees and upper bounds on the largest eigenvalue of any tree (2007, unknown): “Lemma 12 [2].”