Linear Noisy Networks 

 m Other Representations 



In the foregoing analysis we have found all the invariants of a linear 

 noisy network with respect to lossless imbeddings that preserve the 

 number of terminal pairs. With the aid of the impedance formalism, 

 these invariants have been interpreted in terms of the exchangeable power, 

 on the one hand, and in terms of the canonical representation of the 

 network, on the other. There are, however, additional interpretations of 

 the invariants, which are brought out by different matrix representations 

 of the network. For each new representation a characteristic-noise matrix 

 can be defined. As we might expect, all such characteristic-noise matrices 

 have the same eigenvalues, since, after all, these are the only invariants 

 of the network. 



5.1. General Matrix Representations 



The impedance-matrix representation, Eq. 2.6, is conveniently re- 

 written in the form^ 



[i i -^] 



= E 



(5.1) 



where 1 is the identity matrix of the same order as Z. Any other matrix 



^ V. Belevitch, "Four-Dimensional Transformations of 4-pole Matrices with 

 Applications to the Synthesis of Reactance 4-poles," IRE Trans, on Circuit Theory, 

 CT-3, No. 2, 105 (1956). 



33 



