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undergraduate thesis
Dijagonalna i Jordanova forma matrice
2024. urn:nbn:hr:126:052918
Vukalović, Antonio
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Vukalović, A. (2024). Dijagonalna i Jordanova forma matrice (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:052918

Vukalović, Antonio. "Dijagonalna i Jordanova forma matrice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:052918

Vukalović, Antonio. "Dijagonalna i Jordanova forma matrice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:052918

Vukalović, A. (2024). 'Dijagonalna i Jordanova forma matrice', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 10 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:052918

Vukalović A. Dijagonalna i Jordanova forma matrice [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 November 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:052918

A. Vukalović, "Dijagonalna i Jordanova forma matrice", 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:126:052918

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Metadata
TitleDijagonalna i Jordanova forma matrice
Title (english)The Diagonal and Jordan Form of a Matrix
AuthorAntonio Vukalović
MentorDragana Jankov Maširević (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Tema ovog završnog rada je Dijagonalna i Jordanova forma matrice. U radu smo definirali osnovne pojmove linearne algebre, uključujući matrični zapis linearnog operatora, svojstvene vrijednosti, te svojstveni i minimalni polinom. Posebno smo analizirali kako algebarska i geometrijska kratnost svojstvenih vrijednosti utječu na mogućnost dijagonalizacije matrice, te smo kroz primjere prikazali postupak dijagonalizacije. Dokazali smo teorem o tome kada se matrica može dijagonalizirati, kao i druge važne teoreme vezane uz ovu temu. Detaljno smo objasnili teorijsku osnovu Jordanove forme matrice, prikazali metode za njeno određivanje i primijenili ih na konkretne primjere.
Abstract (english)
The topic of this final paper is the Diagonal and Jordan Form of a Matrix. In this paper, we defined the basic concepts of linear algebra, including the matrix representation of a linear operator, eigenvalues, and the characteristic and minimal polynomials. We specifically analysed how the algebraic and geometric multiplicity of eigenvalues affects the possibility of diagonalising a matrix, and we demonstrated the diagonalisation process through examples. We proved the theorem on when a matrix is diagonalisable, as well as other important theorems related to this topic. In the main part of the paper, we thoroughly explained the theoretical foundation of the Jordan form of a matrix, presented methods for its determination, and applied them to specific examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:052918
Study programmeTitle: Bachelor of Mathematics and Computer Science
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2024-09-24 07:18:49