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.