  Positive real odd matrix functions, often referred to as positive real
lossless matrix functions, play an important role in many applications in
multi-port electrical systems. In this paper we present closer analogues to
some of the known results for the scalar, one-port, case in the multi-port
setting. Specifically, we determine necessary and sufficient conditions for the
well studied partial fraction formula to represent functions in the class of
positive real odd matrix functions, and explicit minimal state space
realization formulas for the inverse (admittance) of a function in this class,
which itself is also a positive real odd matrix function. Doing so, enables us
to provide a partial analogue of the poles-zero interlacing behavior from the
scalar case.
