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.