Applications of matrix algebra to network theory
Israel Cederbaum · IEEE Transactions on Information Theory · 1959
In this paper some properties of unimodular (orE-) and paramount (orM-) matrices are discussed. The paper deals with matricesKwhich may be decomposed in a congruenceADA \primewhereAis a rectangular unimodular- andDa 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 matricesAandDor in a proof that such decomposition is impossible. Since the admittance matrices ofn-ports described on pure resistance networks (or RLC networks for positive, real values of the complex frequency) withn + 1nodes, or dually the impedance matrices ofn-ports inscribed intoR-networks with exactlynindependent links belong to the Class ofADA \primematrices the paper defines a method of decomposition of such matrices into the productADA. The synthesis of the correspondingn-port may then be realized by known methods.