  The mathematical theory of quantum feedback networks has recently been
developed by Gough and James \cite{QFN1} for general open quantum dynamical
systems interacting with bosonic input fields. In this article we show, that
their feedback reduction formula for the coefficients of the closed-loop
quantum stochastic differential equation can be formulated in terms of Belavkin
matrices. We show that the reduction formula leads to a non-commutative Mobius
transformation based on Belavkin matrices, and establish a $\star$-unitary
version of the Siegel identities.
