Vektorski produkt na $R^n$

master's thesis

• Author: Matea Pavlek
• Mentor: Ozren Perše (mentor)
• Committee member: Ozren Perše (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Zlatko Drmač (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-11-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu govorimo o egzistenciji vektorskog produkta na $\mathbb{R}^n$. Polazeći od definicije i svojstva vektorskog produkta, pokazujemo da tako definiran vektorski produkt postoji na $\mathbb{R}^n$, 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.

Abstract (english)

In this diploma thesis we consider the existence of cross product on $\mathbb{R}^n$. 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.

• Keywords: vektorski produkt; Hurwitzov teorem; multilinearna funkcija
• Keywords (english): cross product; Hurwitz theorem; multilinear function
• Language: croatian
• URN:NBN: urn:nbn:hr:217:590668
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-29 10:04:02