Let's consider the following block matrix
$$ M = \begin{pmatrix}D&A^T\\A&-D\end{pmatrix},$$
where $A$ and $D$ are $n \times n$ matrices. The diagonal matrix $D$ is defined by $D_{kk} = k \alpha$, where $\alpha \in \Bbb C$. Is there a simple link between the eigenvalues/eigenvectors of the block matrix $M$ and $A$ and $D$?
