so 



where 



PEOFESSOE CATLET ON THE THEOEY OF MATEICES. 



( A, H, G, L ) 



H, B, F, M; 



G, F, C, N 



L, M, N, D 



is the matrix formed with the first minors of 



{a, h, g, I ); 



h, i , f, m 



g, /, c, n 



I, m, n, d 

 moreover 



X=a(l—P -\-nh—mg-{-l, g = bc—f^+nh —mg-\-l, 



[ju=bn—nif+dh — ml , (f=fg — c^+gl — na , 



V =.dg—nl -\-nf — cm , T=hf—bg+ma — Ih , 



and A is the determinant 



(a , h , g , l+l ) 



h , b , f+1, m 



g > /— 15 c , n 

 l—l, m , n , d 



viz., this is 



^ad-P-\-bc-f-\-2(nh^mg)+l. 



a, 'h, g, I 



h, b , f, m 



g, f, c, n 



I, m, n, d 



13. The expression for(T— H)"' is obtained from that of (T + fi)"' by merely trans- 

 posing the terms of the matrix, or, what is the same thing, by changing the signs of 

 X, ««, V, §, cr, T. And it would be easy by means of these developed values to verify the 

 foregoing comparison of (T— Q)(T+Q)~' and (T-fQ)(T — Q,)~\ 



Article Nos. 14 to 22. — Second Investigation. 

 14. I consider from a different point of view the theory of a matrix 



n=( a, b, c, d ) such that !!"'=( p, I, —h, —d), 

 e, /, g 



h 

 i , j, % I 

 m, n, 0, p 

 or, as we may call it, a Hermitian matrix 



, % -g, -c 

 -n, ■'nj, f, b 

 — m, — i, e, a 



