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master's thesis
Primjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:035208
Perković, Matea
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Perković, M. (2018). Primjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2 (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:035208

Perković, Matea. "Primjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:035208

Perković, Matea. "Primjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:035208

Perković, M. (2018). 'Primjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:035208

Perković M. Primjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2 [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:035208

M. Perković, "Primjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:035208

Metadata
TitlePrimjene Hamilton-Cayleyevog teorema na kvadratne matrice reda 2
AuthorMatea Perković
MentorRajna Rajić (mentor)
Committee memberRajna Rajić (predsjednik povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
Committee memberPavle Goldstein (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tema ovog rada je primjena Hamilton--Cayleyevog teorema na kvadratne matrice reda 2. Ovaj diplomski rad sastoji se od dva poglavlja. Prvo poglavlje bavi se poznatim Hamilton--Cayleyevim teoremom, njegovim obratom, svojstvenim vrijednostima i dijagonalizacijom simetričnih realnih matrica, Jordanovom kanonskom formom kompleksnih, realnih i racionalnih matrica, te Jordanovom kanonskom formom nekih posebnih tipova matrica. U drugom poglavlju dajemo formule za izračunavanje \(n\)-te potencije matrica reda 2, proučavamo nizove definirane pomoću sustava linearnih rekurzivnih relacija, rješavamo binomne matrične jednadžbe \(X^n=A\) za matrice drugog reda.
Abstract (english)
The topic of this thesis is application of Hamilton–Cayley’s theorem to square matrices of order 2. This graduate thesis is composed of two chapters. The first one deals with the celebrated Hamilton–Cayley’s theorem, its reciprocal, the eigenvalues and diagonalization of symmetric real matrices, the Jordan canonical form of complex, real and rational matrices, and the Jordan canonical form of some special types of second-order matrices. In the second chapter we give formulae for the calculation of the \(n\)th power of square matrices of order 2, we study sequences defined by systems of linear recurrence relations, we solve binomial matrix equations \(X^n=A\) for second-order matrices.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:035208
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-06-10 11:22:48