34 



ALM AR NÆSS. 



M.-N. Kl. 



1) <) - 



(//-- 1)! ,■ 



2'( 1/^ 'e,<'^ 



f , . . . f , f, : , . . . f« 



fl • ■ ■ f»' - I f''+ I • • • f" 



And as, l)y § 7 (2I, ihf dctc-i-niinant in this fxjjrcssion is cciual to 

 (// — 1 ) ! ^" I f, . . . f, I f, ) 1 . . . f„, it follows immediately from (3) that 

 the -second nicmbci- of the ecjiiation (11) is equal to e/ W/, q. e. d. 



§ II. The space complement of the Ergänzungsdyadic. 



As is known, the „ivtVor" of the i^r^anzun.^sdvadic in .S'., can be 



written : '!' 



i- )• f 



( 1 1 Ü, -= f/>.j - rj a f (c, - ^r.5^ 6 + in. ^ Ä, I C ■ - a b c 



a b c 



The analogous equation h()lds in S,,- We put: 



(2) ^4 = tVX W/. 



1)V § 8151 we get, noticing that here p =^ n — 1, and therefore 



(- \r [n p]l - (— 1)""'^'^(// (/; 11)! I: 



Ü... = e. X \i\ -^ 2^ e, X ((- l)''+ '("-if,... f ^ , f/^ , . . . f„) 



(3) - 2'(- 1,)'^' e, X(<" - 1 f 1 • • • f - I f-^i ■ ■ • f") 



i 



ti • • • f/ - I t'' + 1 • • • t'^ 



= -K-^ ij' + 'e, 



e,- e., 



îi • • • t'- 1 t'-ri • • • Î'' 

 . . . . C« 



fx f. 





We notice that the two-rowed determinants of the first two rows are 

 all scalars of the form : 



(4) 



ij ■ e/ 

 f/ f/ 



Thus we can write: 



./// "./// ^- - (///-//;)• ^<^ 



(5) a = -i*!- D^'+'iy}/-/// 



f. . . • i y . • • i / • • • f' 



f, . . . fi . . . ,f/ . . . f, 



t loc. cit. § 13 (7). 



