Conditions for the impedance and admittance matrices of n-ports without ideal transformers

The matrices relating two adequate systems of simple network co-ordinates of the same network, e.g. node-pair voltages or loop currents, are shown to have all their elements and subdeterminants equal to +1, ¿1 or 0. Any n-port may be looked upon as a part of an adequate system of independent node pairs described on the network or loops inscribed into the network. In the former case the additional node pairs, not included in the n-port, ought to be considered as opencircuited and in the latter case the additional loops ought to be looked on as short-circuited. The conditions for cut-set and loop-incidence matrices are discussed, and then the conditions for impedance and admittance matrices of n-ports without ideal transformers are defined in terms of those incidence matrices. The discussion of the conditions thus derived leads, among other things, to a conclusion that matrices representing pure-resistance n-ports are necessarily such that each principal minor of such a matrix is greater than the modulus of any minor built from the same rows (or columns).