What can I say about the eigenvalues and eigenvectors of the tridiagonal matrix $T$ given as
$T = \begin{pmatrix}
a_1 & b_1 \\
c_1 & a_2 & b_2 \\
& c_2 & \ddots & \ddots \\
& & \ddots & \ddots & b_{n-1} \\
& & & c_{n-1} & a_n
\end{pmatrix}$.
If I set $a_i = 0$, do you know any previous results?
I know some results for simple cases like constant elements or symmetric matrices, but I would like to know if there are any results for more general cases.
Best Answer
It seems that your question has already been answered here:
Eigenvalues of Symmetric Tridiagonal Matrices
No results for general tridiagonal matrices.