Is there a procedure to find the eigenvalues of $\textbf{M}$? $$\begin{eqnarray} \textbf{M}=\left[ \begin {array}{ccccc} \textbf{A} & \textbf{B} & & &\\ \textbf{B}^T & \textbf{ A} & \textbf{B} & &\\ &\ddots &\ddots & \ddots &\\ & & & & \textbf{B} \\ & & & \textbf{B}^T & \textbf{A} \end {array} \right], \end{eqnarray} $$

where $\textbf{B}^T$ is transpose of matrix $\textbf{B}$.