44 



AI.MAR NÆSS. 



M.-X. Kl. 



I »Ilt, f)f course, from this does not follow that the equation holds it 

 we r(iiio\c the o|)eration sig^n (^n. i.e.: tli'j two pol^'adlicls whose space 

 coiuplciiiciits lonii the left ami right iik iiihrr of this equation, are not equal. 



fioiii (1) again follows that, for example I / e, C/ and ^ stands for • • 



(3) 



</ 





e, e., 



e., 



while / > is equal to the same determinant times ( 1)' 

 We also have : 



Ci . . . . îi^ 1 e, + i . 



(4) e,xa = (- i)"(- 1)' + ' 



e„ 



«1 . . . . a,- 1 (h-+\ . 





from which we get: 



(5) /Xa = (- l)"<a. 



In the same way we can prove the more general formula : 



(6) / Xp a^ a.3 .... lip = — (— 1)" ^' <p i\ a,_, . . . . a^. 



We will expand 



X ^^^' 



where and ø' are two dyadics, 0= e, f = x, C/, 0' =e/f'/. 0X '^^' is 

 always a polyadic of order /;. In three-space it is called the vector product 

 of two dyadics. We get : 



(7) <PX^'' ==y->^:X^if'l, :,i^U2. ...>.. 



Here we only consider / ^ J as e,- X ^' — 0- 

 Firstly we assume that i <Cj. Then we have: 



(8) e,- X e/ 



. e. 



ei 



1 







i'+/ 



,^i 



C;, 



ei 



e„ 



If / ^ J we get : 



(9) 



e/Xe; - (- ir-i^/. 



