Quite stuck with the following question:
Find the eigenvalues and eigenvectors of:
$\begin{bmatrix}-2 & 1 &0& ......&0\\1 & -2 & 1&......&0\\0&1&-2&......&.\\.&.&.&......&.\\.&.&.&......&1\\.&.&.&1&-2\end{bmatrix}$
Where the matrix is $n \times n$.
Problems:
I found the eigenvalues for the two and three dimensional case as being $\lambda= -1,-3$ and something different for the three dimensional case so I had no idea how to generalize to n dimensions. Any help would be appreciated.