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master's thesis
Spektar matrice
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:722570
Gakić, Ante
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Gakić, A. (2024). Spektar matrice (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:722570

Gakić, Ante. "Spektar matrice." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:722570

Gakić, Ante. "Spektar matrice." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:722570

Gakić, A. (2024). 'Spektar matrice', Master's thesis, University of Zagreb, Faculty of Science, accessed 27 September 2024, https://urn.nsk.hr/urn:nbn:hr:217:722570

Gakić A. Spektar matrice [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 September 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:722570

A. Gakić, "Spektar matrice", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:722570

Metadata
TitleSpektar matrice
Title (english)Spectrum of matrices
AuthorAnte Gakić
MentorLjiljana Arambašić (mentor)
Committee memberLjiljana Arambašić (predsjednik povjerenstva)
Committee memberGoran Igaly (član povjerenstva)
Committee memberVeronika Pedić Tomić (član povjerenstva)
Committee memberMatej Mihelčić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-07-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj diplomski rad istražuje spektar matrica, počevši od temeljnih pojmova za linearne operatore na konačnodimenzionalnim vektorskim prostorima i analognih tvrdnji za matrice. Zatim se istražuju metode računanja svojstvenih vrijednosti, uključujući razne oblike metode potencija i teorem o Geršgorinovim krugovima koji određuje položaj svojstvenih vrijednosti u kompleksnoj ravnini. Konačno, prikazuju se praktične primjene svojstvenih vrijednosti na pojednostavljenim modelima Markovljevih lanaca, matričnog modela rasta populacije, sustava rangiranja sportskih timova te Googleovog algoritma za sortiranje rezultata pretraživanja.
Abstract (english)
This thesis delves into the spectrum of matrices, starting with fundamental concepts for linear operators on finitedimensional vector spaces and analogous statements for matrices. It then investigates methods for calculating eigenvalues including various forms of the power method and Gerschgorin's Disk Theorem that locates the eigenvalues in the complex plane. The thesis concludes by presenting the practical applications of eigenvalues in simplified models of Markov chains, matrix population growth model, sports team ranking systems, and Google's PageRank algorithm for organizing search results.
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:217:722570
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-07-24 11:23:15