438 



MOORE AND PHILLIPS. 



There on n such equations. EHminating R2...Rn as in solving 

 algebraic equations, we get 



= A-i?i = 



Similarly, 



&11$ — Oii^, 621*^ — (l2i^,. . ., 6„i$ — (Inl^ 

 612$ — ai2^, 1)22^ — a22^, . ., bn2^ — an2^ 



bl„^ — am^, bnn^ — ttnn^ 



0. 



A-i?2 = A-i?3 =... = A-Rn 



Since i?i, . . .Rn on linearly independent, 



A = 0. 

 when expanded this has the form 



The coefficient Ao is the discriminant of "^, and A „ that of ^. Hence, 

 if either of the dyadics is non-singular, the coefficients do not all 

 vanish. In particular, if ^ is an idemfactor, the equation becomes 



Ao^^ + A,^--' + . . .+.4„_i$ + AnI = 0. 



This is the Hamilton-Cayley equation satisfied by $. 



