Eigenvalues and eigenvectors of tridiagonal matrices

Abstract

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 WenChyuan 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.