Matrix Operations Induced by Network Connections
William N. Anderson, R. J. Duffin, George E. Trapp · SIAM Journal on Control · 1975
The interconnection of two electrical networks is used to define an operation, called the router sum, on the corresponding impedance matrices. For the special case of the series connection, the router sum is the ordinary matrix sum ; for the parallel connection, the parallel sum is obtained [3]. General connections are considered in this paper. Conditions for commutativity and associativity of the router sum are given. Inequalities related to minimizing power are proved. An explicit formula for the router sum is given in terms of the shorted operator [2].