24 



ALM AK NÆ.SS, 



M.-N. Kl. 



arc k.^, /•)( . . . .kp, which arc all lo the right of the column /•,. Hence 

 tile tlcmciit 1 ill the first row also in this determinant belongs to the 

 coluinii ky. The \aliic of tin; (i(t<iininant therefore is 



(8) 



(- 1) 



ii\ + 1 







-(-1) 



ii\-\-\ 



Mcnce the final sign of the expression iD) is: 



(9) 



(- 1) 



n- -\- n 



p~ -\- II -\- p -j- tt2 -\- ti 



1 



- 1 k--i-\+ki 

 2 





= (—1) 1 =(-1) " 1 



since jr + /; + 2 lv\ is an even number, and therefore cancel out. Then we get: 



10) e^M X 



Ci . . .,^k-. . . Cr 



^l 



e„ 



1) 



^^^+.-v., 



1 {n — p) ! 



ex.2 

 ik2 



CA: 



e>t. 



The scalar factor belonging to this term is: 



(E) 



(-1) 



,P^PSEZJ1 + ^,^ 



' Vki 



(h '(•I 



^1 1.' 



Opin 



(hk. 



where we can write V • <ik\ instead of Vki. Multiplying by this scalar, the 

 term ( 1 0) takes the following form : 



(F) 



(- O'^ + 'l^-^ilv-e^, 



Ck. 



Ck^ 



«1 /ti 



i^pk\ 



When we now form the space complement : 



Ci . . . /k. . . . e« 



(G) 



ex. X' 



<-'l 



e„ 



^'i k^ 



Opk^ 



we, of course, get an expression which can be obtained from (Di by in- 

 terchanging lx\ with A,, only it must be noticed that the single „one" in the 

 first row (of the last determinant of (Di) belongs to the column ko — 1, 

 because, in forming this determinant from the last // — p + 1 rows of (7), 

 we have also stricken out the X\"^ column, which is to the left of /("o- Thus 

 the value of the „one-determinant" in this case (compare (8)) is 



