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undergraduate thesis
Kvadratna forma
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:337729
Panenić, Lorana
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Panenić, L. (2024). Kvadratna forma (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:337729

Panenić, Lorana. "Kvadratna forma." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:337729

Panenić, Lorana. "Kvadratna forma." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:337729

Panenić, L. (2024). 'Kvadratna forma', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:337729

Panenić L. Kvadratna forma [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:337729

L. Panenić, "Kvadratna forma", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:337729

Metadata
TitleKvadratna forma
Title (english)Quadratic Forms
AuthorLorana Panenić
MentorIvan Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu bavimo se kvadratnim formama, njihovim glavnim svojstvima te problemom uvjetne optimizacije. Najprije su definirane simetrična matrica i kvadratna forma te potom na primjerima ilustrirana njihova veza. Nadalje je opisan postupak zamjene varijabli kod kvadratnih formi. Iskazan je teorem o glavnim osima i pokazana njegova geometrijska interpretacija. Definirane su pozitivno definitna, negativno definitna i indefinitna kvadratna forma te je teoremom opisana njihova veza sa svojstvenim vrijednostima matrice kvadratne forme. Na koncu je, nizom primjera i teorema, analiziran problem uvjetne optimizacije kvadratnih formi.
Abstract (english)
This paper explores quadratic forms, their key properties, and the problem of constrained optimization. It begins with the definitions of symmetric matrices and quadratic forms, followed by examples illustrating their relationship. The procedure for variable substitution in quadratic forms is then described. The theorem on principal axes is stated and its geometric interpretation is provided. Positive definite, negative definite, and indefinite quadratic forms are defined, and their connection to the eigenvalues of the associated matrices is explained through a theorem. Finally, the problem of constrained optimization of quadratic forms is analyzed through a series of examples and theorems.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:337729
Study programmeTitle: University Bachelor of Mathematics (univ. bacc. math.)
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 on2024-10-15 09:51:01