ELA, Volume 15, pp. 115-133, April 2006, abstract.

Eigenvalues and Eigenvectors of Tridiagonal Matrices

Said Kouachi

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.