# Find the eigenvalues the block matrix $M=\begin{bmatrix}A+2D & A \\ A & D \end{bmatrix}$

Let $A$ be any square matrix with eigenvalues $\lambda_1,\lambda_2,\cdots,\lambda_n$ and $D$ is a diagonal matrix with entries $d_1,d_2,\cdots,d_n$, then how can one find the eigenvalues of the following block matrix?

$$M=\begin{bmatrix}A+2D & A \\ A & D \end{bmatrix}$$

• Is there any relation between $A$ and $D$? For example, are the diagonal entries of $D$ the row sums of $A$? – M. Vinay Jun 24 '16 at 7:44
• yes of course because $A$ is adjacency matrix of graph and $D$ is degree matrix – kalpeshmpopat Jun 24 '16 at 7:51
• Does the answer at math.stackexchange.com/questions/54133/… help? – almagest Jun 24 '16 at 10:08
• It is very much helpful – kalpeshmpopat Jun 24 '16 at 10:37