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undergraduate thesis
Spektralna teorija normalnih operatora
2019. urn:nbn:hr:126:076879
Juzbašić, Lara
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Geometry and Mathematics Teaching Mathematics Research Group

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Juzbašić, L. (2019). Spektralna teorija normalnih operatora (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:076879

Juzbašić, Lara. "Spektralna teorija normalnih operatora." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:076879

Juzbašić, Lara. "Spektralna teorija normalnih operatora." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:076879

Juzbašić, L. (2019). 'Spektralna teorija normalnih operatora', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:076879

Juzbašić L. Spektralna teorija normalnih operatora [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2025 January 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:076879

L. Juzbašić, "Spektralna teorija normalnih operatora", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:076879

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Metadata
TitleSpektralna teorija normalnih operatora
Title (english)Spectral Theory of Normal Operators
AuthorLara Juzbašić
MentorSuzana Miodragović (mentor)
MentorMarija Miloloža Pandur (komentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Geometry and Mathematics Teaching Mathematics Research Group)
Osijek
Defense date and country2019-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu proučavamo normalne operatore i njihova spektralna svojstva. U prva tri poglavlja navest ćemo osnovne pojmove, definirati projektore i spomenuti njihova svojstva te objasniti vezu normalnog operatora s dekompozicijom jedinice. Nakon toga, Cayleyevim transformacijama povezat ćemo hermitske i unitarne operatore te proširiti pojam adjungiranog operatora. U posljednja dva poglavlja objasnit ćemo konstrukciju projektora na područje vrijednosti operatora te upoznati se s pojmom kvazi inverznog operatora i njegovom primjenom kod rješavanja problema najmanjih kvadrata.
Abstract (english)
In this bachelor’s thesis we will consider normal operators and their spectral properties. In the first three chapters we will investigate basic concepts, define projections and mention their properties. After that, we will connect Hermitian and unitary operators by Cayley transformations, and expand the concept of an adjoint operator. In the last two chapters the construction of a projection onto the image of an operator will be explained, and the concept of a generalized inverse and its usage in solving the least squares problem will be introduced.
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:126:076879
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-10-16 06:50:38