178 BELL SYSTEM TECHNICAL JOURNAL 



As an example of the application of these formulas we assume that G and 

 H are expressed in terms of the F's. Then we may take K and L' to be 

 particular choices of P and P and equation (A5.9) becomes 



FioPAP"' - FiaPA"'?"' = (P')~'EP'\ 



From equations (2.59) and (2.62) 



Yo +Yo= YuPAP'' - VnPA-'p-' 



and hence 



P'(F,+ Yo)P = E. 



For the more general choice of P and P allowed in §2.8 the diagonal matrix 

 E is replaced by a general diagonal matrix. Similarly it follows that 



Q'{Zo + Z,)Q 



is a diagonal matrix. 



