OF A BIPARTITE QUADRIC FUNCTION. 
505 
153] 
17. Hence, finally, we have the following Theorem for the automorphic linear 
transformation of the bipartite quadric, 
(G#®, y> y, z), 
when the two transformations are identical, viz. if T / be a skew symmetrical matrix, 
and if 
T = - (i-in- 1 + tr. - tr. + T,; 
then if 
y, «) = (H-i(il-T)(0 + T)“*il$« /f y„ z), 
(x, y, z) = (il -1 (il — T) (i2 + T) -1 il^ X/ , y /f Z/ ); 
we have 
(&&> y> z ) = ( a fa,> Vn ^5 x /> y„ z,); 
and in particular, 
If O is a symmetrical matrix, then T is an arbitrary skew symmetrical matrix ; 
If XI is a skew symmetrical matrix, then T is an arbitrary symmetrical matrix. 
C. II. 
64