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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 $c$.

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    @Stuart As the OP has approved your answer, please consider converting your comment into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2013-06-14

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