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master's thesis
Strukture bilinearnih formi
2023. urn:nbn:hr:126:529069
Rečić, Ivana
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Rečić, I. (2023). Strukture bilinearnih formi (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:529069

Rečić, Ivana. "Strukture bilinearnih formi." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:529069

Rečić, Ivana. "Strukture bilinearnih formi." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:529069

Rečić, I. (2023). 'Strukture bilinearnih formi', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 15 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:529069

Rečić I. Strukture bilinearnih formi [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 November 15] Available at: https://urn.nsk.hr/urn:nbn:hr:126:529069

I. Rečić, "Strukture bilinearnih formi", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:529069

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Metadata
TitleStrukture bilinearnih formi
Title (english)Structures Of Bilinear Forms
AuthorIvana Rečić
MentorIvan Matić (mentor)
Committee memberDragana Jankov Maširević (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberTomislav Marošević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-10-04, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom diplomskom radu iskazuju se aksiomi koji su potrebni kako bi se preslikavanje definiralo kao bilinearna forma te se obrađuju tri glavne vrste bilinearnih formi, a to su simetrične, hermitske i alternirajuće. U uvodnom dijelu se nalazi kraći prikaz definicija i rezultata koji su važni za temu rada te nešto više o uređenim poljima. U dijelu o simetričnim formama definiraju se ortogonalne baze te dijagonalizibilna matrica i ti se pojmovi povezuju sa simetričnom formom. Osim toga, obrađuju se simetrične forme nad uređenim poljem te se prikazuje Gram-Schmidtov postupak ortogonalizacije. U dijelu o hermitskim formama navode se rezultati ekvivalentni onima u simetričnom slučaju te se iskazuje i dokazuje spektralni teorem u hermitskom i simetričnom slučaju. U dijelu o alternirajućim formama definiraju se pojmovi hiperboličke ravnine, hiperboličkog para te standardne alternirajuće matrice koji se povezuju s navedenom formom.
Abstract (english)
This thesis presents the axioms necessary to define mapping as a bilinear form. Furthermore, it discusses the three main types of bilinear forms, namely symmetric, hermitian, and alternating. In the introductory part, there is a brief presentation of definitions and results that are important for the topic of the paper, as well as some more information about ordered fields. In the section on symmetric forms, orthogonal bases and a diagonalizable matrix are defined and connected to the symmetric form. In addition, symmetric forms over the ordered field are processed and the Gram-Schmidt orthogonalization procedure is presented. In the section on hermitian forms, results equivalent to those in the symmetric case are given, and the spectral theorem is stated and proved in the hermitian and symmetric cases. In the section on alternating forms, the concepts of hyperbolic plane, hyperbolic pair, and standard alternating matrix, which are associated with the aforementioned form, are defined.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:529069
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical 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 on2023-11-07 10:20:18