My question is a really straightforward one: Is there an easier way to find the eigenvalues and/or eigenvectors of a 2x2 block diagonal matrix other than direct diagonalization of the whole matrix?
$ \left( \begin{array}{ccc} A & 0 \\ 0 & B \end{array} \right )$
Here $A$, $B$ are $n \times n$ symmetric matrices.