Applications of matrix algebra to network theory

In this paper some properties of unimodular (or
E
-) and paramount (or
M
-) matrices are discussed. The paper deals with matrices
K
which may be decomposed in a congruence
ADA \prime
where
A
is a rectangular unimodular- and
D
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
A
and
D
or in a proof that such decomposition is impossible. Since the admittance matrices of
n
-ports described on pure resistance networks (or RLC networks for positive, real values of the complex frequency) with
n + 1
nodes, or dually the impedance matrices of
n
-ports inscribed into
R
-networks with exactly
n
independent links belong to the Class of
ADA \prime
matrices the paper defines a method of decomposition of such matrices into the product
ADA
. The synthesis of the corresponding
n
-port may then be realized by known methods.