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master's thesis
Blok-matrice
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:170686
Tomić, Domagoj
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Tomić, D. (2024). Blok-matrice (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:170686

Tomić, Domagoj. "Blok-matrice." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:170686

Tomić, Domagoj. "Blok-matrice." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:170686

Tomić, D. (2024). 'Blok-matrice', Master's thesis, University of Zagreb, Faculty of Science, accessed 24 August 2024, https://urn.nsk.hr/urn:nbn:hr:217:170686

Tomić D. Blok-matrice [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 August 24] Available at: https://urn.nsk.hr/urn:nbn:hr:217:170686

D. Tomić, "Blok-matrice", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:170686

Metadata
TitleBlok-matrice
Title (english)Block-matrix
AuthorDomagoj Tomić
MentorLjiljana Arambašić (mentor)
Committee memberLjiljana Arambašić (predsjednik povjerenstva)
Committee memberMarko Radulović (član povjerenstva)
Committee memberIvana Šain Glibić (član povjerenstva)
Committee memberSnježana Lubura Strunjak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-05-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu istražujemo koncept blok-matrice. Svaku matricu možemo podijeliti na manje matrice, koje nazivamo blokovima ili podmatricama, pomoću vodoravnih i okomitih linija. Na taj način možemo pojednostaviti neke račune s matricama velikih formata, te dokaze za određene tvrdnje s matricama provesti na jednostavniji i pregledniji način. Prvo poglavlje obrađuje osnove matrica, elementarne transformacije nad njima te postupke za određivanje inverza, determinante i ranga. Drugo poglavlje fokusira se na blokmatrice, istražujući iste koncepte i primjenjujući ih na blok-matrice. Nakon toga, primjenjujemo naučene tehnike za odredivanje ranga produkta i zbroja matrice te istražujemo veze izmedu spektara matrica AB i BA.
Abstract (english)
In this thesis, we explore the concept of block-matrix. We can divide each matrix into smaller matrices, which we call blocks or submatrices, using horizontal and vertical lines. In this way, we can simplify some calculations with large-format matrices, and carry out proofs for certain assertions with matrices in a simpler and more transparent way. The first chapter deals with the basics of matrices, elementary transformations over them and procedures for determining the inverse, determinant and rank. The second chapter focuses on block matrices, exploring the same concepts and applying them to block matrices. After that, we apply the learned techniques to determine the rank of the matrix product and sum, and investigate the connections between the spectra of the matrices AB and BA.
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:217:170686
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 on2024-05-21 14:29:40