Blok-matrice

master's thesis

• Title (english): Block-matrix
• Author: Domagoj Tomić
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Marko Radulović (član povjerenstva)
• Committee member: Ivana Šain Glibić (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-05-02, 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: osnove matrica; elementarne transformacije; određivanje inverza; determinante; rang
• Language: croatian
• URN:NBN: urn:nbn:hr:217:170686
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-05-21 14:29:40