I have a $ m \times m$ matrix, $A$, of the following form:
$$A=\left( \begin{array} {c,c} A' \quad \vec{\delta} \\ \vec{\delta}^T \quad \varepsilon \end{array} \right)$$
wher $\vec{\delta}$ is a $(m-1) \times 1 $ column vector of $\delta$'s. $A'$ is a $(m-1) \times (m-1)$ matrix of the following form:
$$ A' = b J_{m-1} + (a-b) I_{m-1}. $$
Here $J_{m-1}$ is a $(m-1) \times (m-1)$ matrix of all one's and $I_{m-1}$ is the $(m-1) \times (m-1)$ identity matrix Hence $A'$ is a matrix with all $a$'s on the diagonal and all $b$'s off-diagonals.
I would like to compute the eigenvalues of $A$. What's the best way to compute these eigenvalues?