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The Representation Themen of Linear Functionals and Hermitian Adprint Operators
Sanja Stjepanović (2018)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Numerical Mathematics Research Group
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Stjepanović, S. (2018). Reprezentacija linearnog funkcionala i hermitsko adjungiranje (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:387545

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

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

Stjepanović, S. (2018). 'Reprezentacija linearnog funkcionala i hermitsko adjungiranje', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 20 February 2019, https://urn.nsk.hr/urn:nbn:hr:126:387545

Stjepanović S. Reprezentacija linearnog funkcionala i hermitsko adjungiranje [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2019 February 20] Available at: https://urn.nsk.hr/urn:nbn:hr:126:387545

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

Metadata
TitleReprezentacija linearnog funkcionala i hermitsko adjungiranje
AuthorSanja Stjepanović
Mentor(s)Suzana Miodragović (thesis advisor)
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.
KeywordsUnitary and normed spaces linear operator isomorphism antilinear mapping conjugate space linear functional Riesz representation theorem Representation theorem of a linear functional Hermitian adjoint
Parallel title (English)The Representation Themen of Linear Functionals and Hermitian Adprint Operators
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Applied Mathematics
Numerical Mathematics Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Algebra
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2018-09-11
Parallel 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.
Parallel keywords (Croatian)Unitarni i normirani prostori linearan operator izomorfizam antilinearno preslikavanje konjugirani prostor lineani funkcional Rieszov teorem o reprezentaciji funkcionala Teorem o reprezentacij linearnog funkcionala Hermitski adjungirani operator.
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:387545