Sličnost matrica

master's thesis

• Author: Ana Međimurec
• Mentor: Dijana Ilišević (mentor)
• Committee member: Dijana Ilišević (predsjednik povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-11-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Za matrice \(A, B\in M_n(\mathbb{F})\) kažemo da su slične nad poljem \(\mathbb{F}\) ako postoji regularna matrica \(P\in M_n(\mathbb{F})\) takva da je \(B=P^{-1}AP\). U ovom diplomskom radu izloženi su različiti nužni i dovoljni uvjeti za sličnost matrica. Sličnost matrica promatramo kao moćan alat za transformaciju matrica u što jednostavniji oblik, misleći pritom na dijagonalne ili trokutaste matrice.

Abstract (english)

Matrices \(A, B\in M_n(\mathbb{F})\) are said to be similar over a field \(\mathbb{F}\) if there exists an invertible matrix \(P\in M_n(\mathbb{F})\) such that \(B=P^{-1}AP\). In this thesis various necessary and sufficient conditions for the similarity of matrices are presented. We consider the similarity of matrices as a powerful tool for transforming matrices into simpler forms, like diagonal or triangular matrices.

• Keywords: matrica; dijagolane matrice; trokutaste matrice
• Keywords (english): matrix; diagonal matrices; triangular matrices
• Language: croatian
• URN:NBN: urn:nbn:hr:217:267584
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2020-10-10
• Created on: 2020-07-10 10:01:47