Consider a $N \times N$ hermitian matrix $A$. Consider a complex $N \times 1$ vector $b$ and positive constant $c$. Given $A$ (hence its eigen-values), can we find the eigen-values of the following matrix. \begin{align} B=\begin{bmatrix} A & b \\ b' & c \end{bmatrix} \end{align}
in terms of those of $A$ (or $A$'s entries) and, $b$ and $c$.