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master's thesis
Neke primjene linearne algebre u geometriji
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:123779
Jurić, Manuela
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Jurić, M. (2018). Neke primjene linearne algebre u geometriji (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:123779

Jurić, Manuela. "Neke primjene linearne algebre u geometriji." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:123779

Jurić, Manuela. "Neke primjene linearne algebre u geometriji." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:123779

Jurić, M. (2018). 'Neke primjene linearne algebre u geometriji', Master's thesis, University of Zagreb, Faculty of Science, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:123779

Jurić M. Neke primjene linearne algebre u geometriji [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:217:123779

M. Jurić, "Neke primjene linearne algebre u geometriji", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:123779

Metadata
TitleNeke primjene linearne algebre u geometriji
AuthorManuela Jurić
MentorMarko Erceg (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
Committee memberPavle Goldstein (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-07-17, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu prikazane su samo neke od mnogobrojnih primjena linearne algebre u matematici, posebno u geometriji. Iskazana je Cauchy - Bunjakovski - Schwarzova nejednakost na unitarnim prostorima, te su prezentirana četiri različita dokaza. Potom je prikazana njena važnost na nekoliko primjera iz geometrije (na primjer, definicija kuta u realnom unitarnom prostoru, određivanje maksimuma funkcije). Iskazan je i dokazan Mazur - Ulamov teorem koji karakterizira izometrije (realnih) unitarnih prostora, odnosno daje dovoljne uvjete uz koje su izometrije nužno linearna preslikavanja. Primjena opisanih izometrija je pokazana na dva primjera u ravnini pri svođenju krivulja drugog reda na kanonski oblik.
Abstract (english)
In this thesis the focus is on presenting some of many applications of linear algebra in mathematics, particularly in geometry. The Cauchy - Bunjakovski - Schwarz inequality on unitary (inner product) spaces is stated and four different proofs are given. The importance of this inequality is shown on four examples (e.g.~definition of the angle in real unitary spaces, maximisation of functions under certain constraints). The Mazur - Ulam theorem is stated and a proof presented. By this theorem a characterisation of all isometries on (real) unitary spaces is given, i.e.~sufficient conditions on isometries to be linear mappings are provided. The use of above isometries is shown on two examples on the plane transforming second-order curves into their canonical form.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:123779
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-11-29 12:03:57