Abstract
It has been found that interesting mathematical relationships arise from a vectorial generalization of Kirchhoff's and Ohm's laws, in which the “resistors” become Hermitian positive semidefinite (PSD) linear operators. In analogy to the parallel connection of resistors Anderson and Duffin studied the parallel sum R : S of two PSD operators on a finite dimensional space, defined by R : S = R(R + S) †S . Duffin and Trapp then studied the hybrid connection. This paper generalizes some of their results to a much broader class of electrical connections.
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