I have the feeling that the following expression can be simplified, however i cannot find a way...
$\frac{|\mathbf{b}^H \mathbf{A} \mathbf{c}|^2}{\mathbf{c}^H \mathbf{A} \mathbf{c}}$ with
$\mathbf{A} \in \mathbb{C}^{N \times N}, \mathbf{A} \geq \mathbf{0}$ positive semidefinite
$\mathbf{b}, \mathbf{c} \in \mathbb{C}^{N \times 1}$
This is part of an optimization problem over $\mathbf{A}$.