OF ARTS AND SCIENCES. 



51 



Now, by reference to the theorem referred to above, it will be 

 seen that if <£ is the most general matrix commutative with £2, 

 then <f> may be written as w^w -1 where 



= c 



D. 



in which all the constituents are zero except those in the squares 

 Vi> Vv e tc, along the principal diagonal, and these square arrays or 

 subsidiary matrices are of order equal respectively to the order of 

 the subsidiary matrices V 6 2 , etc., to which they severally corre- 

 spond; moreover, 



Vi - 



m 



fin 



V2 



In 



etc., etc. 



