Reprezentacija linearnog funkcionala i hermitsko adjungiranje

Stjepanović, Sanja

undergraduate thesis

Reprezentacija linearnog funkcionala i hermitsko adjungiranje

Stjepanović, Sanja (2018)

Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Numerical Mathematics Research Group

Cite this document

APA 6th Edition

Stjepanović, S. (2018). Reprezentacija linearnog funkcionala i hermitsko adjungiranje (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:387545

MLA 8th Edition

Stjepanović, Sanja. "Reprezentacija linearnog funkcionala i hermitsko adjungiranje." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:387545

Chicago 17th Edition

Harvard

Stjepanović, S. (2018). 'Reprezentacija linearnog funkcionala i hermitsko adjungiranje', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 14 August 2020, https://urn.nsk.hr/urn:nbn:hr:126:387545

Vancouver

Stjepanović S. Reprezentacija linearnog funkcionala i hermitsko adjungiranje [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2020 August 14] Available at: https://urn.nsk.hr/urn:nbn:hr:126:387545

IEEE

S. Stjepanović, "Reprezentacija linearnog funkcionala i hermitsko adjungiranje", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:387545

Cite this item: https://urn.nsk.hr/urn:nbn:hr:126:387545

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Metadata

Title	Reprezentacija linearnog funkcionala i hermitsko adjungiranje
Title (english)	The Representation Themen of Linear Functionals and Hermitian Adprint Operators
Author	Sanja Stjepanović
Mentor	Suzana Miodragović (mentor)
Granter	Josip Juraj Strossmayer University of Osijek Department of Mathematics (Chair of Applied Mathematics) (Numerical Mathematics Research Group) Osijek
Defense date and country	2018-09-11, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics Algebra
Abstract	Ovaj rad predstavlja teoriju koja vodi do iskaza i dokaza Teorema o reprezentaciji linearnog funkcionala pomoću kojeg ćemo uvest pojam hermitski adjungiranih operatora. U radu ćemo se prvo osvrnuti na unitarne i normirane prostore te pojmove koji se na njima definiraju kao što su okomitost vektora, ortogonalni komplement i normiranost vektora. Zatim ćemo definirati linearne operatore i, sa njima usko povezane, antilinearne operatore te proučiti njihove razlike. Nadalje, objasniti ćemo što su to monomorfizmi, epimorfizmi i izomorfizmi, te navesti kriterije i dodatne uvijete pomoću kojih ih možemo raspoznati ili čak poistovjetiti. Osim toga, obraditi ćemo konjugirane prostore koje možemo pridružiti proizvoljnim vektorskim prostorima te se uz primjere dotaći linearnih funkcionala i izreći Rieszov teorem o reprezentaciji funkcionala koji nam omogućuje jedinstven zapis funkcionala. Na kraju rada ćemo se posvetiti hermitski adjungiranom operatoru i njegovim svojstvima.
Abstract (english)	This paper represents the theory leading up to the Representation theorem of a linear functional, which we will use later to introduce the Hermitian adjoint operators. The paper first introduces unitary and normed vector spaces and mentions some terms accompanying them such as orthogonal vectors, orthogonal complements and the norm of a vector. Afterwards we will define linear and antilinear operators, which are closely related, and analyze the differences between them. Furthermore, we will explain what monomorphisms, epimorphisms and isomorphisms are, and mention different criteria and additional conditions for identifying them or even make them indistinguishable. We will also consider conjugate spaces of a vector space and, through examples, touch upon the subject of linear functionals and state the Riesz representation theorem which enables us to have a unique depiction of a functional. The end of this paper will be reserved for the explanation of the Hermitian adjoint and its properties.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:126:387545
Study programme	Title: 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 resource	Text
File origin	Born digital
Access conditions	Open access
Terms of use
Created on	2018-10-18 09:07:37