Applications of matrix algebra to network theory

In this paper some properties of unimodular (or -) and paramount (or -) matrices are discussed. The paper deals with matrices which may be decomposed in a congruence where is a rectangular unimodular- and a diagonal- matrix with constant, positive and real diagonal elements. It is shown that such a decomposition, if at all possible, is essentially unique and a direct algebraic procedure is given which results either in finding the pair of matrices and or in a proof that such decomposition is impossible. Since the admittance matrices of -ports described on pure resistance networks (or RLC networks for positive, real values of the complex frequency) with nodes, or dually the impedance matrices of -ports inscribed into -networks with exactly independent links belong to the Class of matrices the paper defines a method of decomposition of such matrices into the product . The synthesis of the corresponding -port may then be realized by known methods.