University of Zagreb. Faculty of Science. Department of Mathematics.
Abstract
U ovom radu govorimo o egzistenciji vektorskog produkta na Rn. Polazeći od definicije i svojstva vektorskog produkta, pokazujemo da tako definiran vektorski produkt postoji na Rn, samo za n=0,1,3 i 7. Nadalje, koristeći Hurwitzov teorem, dajemo i alternativni dokaz te tvrdnje. Na kraju, pokazujemo u kojim slučajevima postoji vektorski produkt kao multilinearna funkcija.In this diploma thesis we consider the existence of cross product on Rn. Starting from the definition and properties of cross product, we show that such cross product exists only for n=0,1,3 and 7. Furthermore, using the Hurwitz theorem, we give an alternative proof of that claim. Ultimately, we show in which cases does cross product, defined as a multilinear function, exists