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master's thesis
Ortogonalnost u normiranim prostorima
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:465053
Končić, Mihael
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Končić, M. (2019). Ortogonalnost u normiranim prostorima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:465053

Končić, Mihael. "Ortogonalnost u normiranim prostorima." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:465053

Končić, Mihael. "Ortogonalnost u normiranim prostorima." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:465053

Končić, M. (2019). 'Ortogonalnost u normiranim prostorima', Master's thesis, University of Zagreb, Faculty of Science, accessed 02 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:465053

Končić M. Ortogonalnost u normiranim prostorima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 December 02] Available at: https://urn.nsk.hr/urn:nbn:hr:217:465053

M. Končić, "Ortogonalnost u normiranim prostorima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:465053

Metadata
TitleOrtogonalnost u normiranim prostorima
AuthorMihael Končić
MentorTomislav Berić (mentor)
Committee memberTomislav Berić (predsjednik povjerenstva)
Committee memberBoris Guljaš (član povjerenstva)
Committee memberDamir Bakić (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu bavili smo se pitanjem poopćenja ortogonalnosti na normirane prostore u kojima općenito ne postoji skalarni produkt. Za početak smo definirali osnovne pojmove vezane za unitarne i normirane prostore te vezu između njih. Također smo uveli šest svojstava koje klasična ortogonalnost zadovoljava na unitarnom prostoru. U drugom poglavlju navodimo različite definicije poopćenja ortogonalnosti u normiranim prostorima. Svako od tih poopćenja smo posebno komentirali, pokazali da se zaista radi o poopćenju te provjerili koja od šest svojstva ortogonalnosti su zadovoljena. U posljednjem poglavlju bavili smo se pitanjem koliko je neki normiran prostor daleko od toga da bude unitaran, stoga smo uveli neke konstante kojima možemo mjeriti ta odstupanja.
Abstract (english)
In this graduate thesis we discussed the problem of generalised orthogonalities in normed spaces where an inner product may not exist. Firstly we introduced basic definitions related to inner product and normed spaces as well as the connection between the two. We have also introduced six properties which the classical definition of orthogonality in inner product spaces satisfies. In second chapter various definitions of generalized orthogonality in normed spaces were introduced. We debated each one of these orthogonalities separately, proved that they really are generalised orthogonalities and we also checked which orthogonality properties they satisfy. In the last chapter we discussed how close is a normed space to being a Hilbert space. To that end some constants which measure those deviations were introduced.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:465053
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-02-06 11:13:29