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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?

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

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

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