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.



Eigenvalues and eigenvectors of tridiagonal matrices
It seems that your question has already been answered here:


[Eigenvalues of Symmetric Tridiagonal Matrices](https://mathoverflow.net/questions/131527/eigenvalues-of-symmetric-tridiagonal-matrices)


No results for general tridiagonal matrices.


