Let $A$ be an $n*n$ real-symetric matrix, B be a $p*n$ real matrix and $\eta$ be a real number. I want to know if we can give an upper bound of the following inverse matrix $G={\begin{pmatrix} A-i\eta I_n & B^T\\ B & -I_p \end{pmatrix}}^{-1}$.
It's easy to see that if $p=0$, then $||G||\leq \eta^{-1}$. But when $p$ is not $0$, how can I give an upper bound of the norm? Does anybody have any ideas or references about this problem?
Any help is appreciated.