42 



AI.MAK N/KSS. 



M.-X. Kl. 



analogous way as the vector product does in the |)ai-ii(uhir case that we 

 have three equations with three unknowns, t 



Written in full, (9) becomes: 



1 



[71 





/«1 



./i M- 1 /2 '' + I f» ' — 



A" Â" 



J un 



which is the usual form. 



Another related application shall also be mentioned: 

 Let there be given the two systems of independent vectors f, and f/. We 

 will find the dyadic A' which transforms the vectors f,- into the vectors f/ 

 respectively. A' is hereby completely determined by the // equations: 



llj 



^•f^=-f:^ 



Let — ^i, f , ^ x{ e,, else the notations given above. From (11) we 

 then get : 



(12) X-f e, = f/e/ 



(13) or: 



Multiplying by 'P* we get 



(14) 



( 1 5) or : 



whereby A' is determined. 



Let us put : 



(16) then, by (15) 



X ■ (Pc = <Pc' 

 X • (Pc ■ <P* = <Pc' ■ <P* 



X - 0/ • (p* 



X = e,- ):,■ = e,- C/ .v, 



171 



x,i e/ - r^ 





t C. Runge: Vektoranalysis (des dreidimensionalen Raumes!, (Leipzig 1919t § 12. 



