Matrične potence

delo diplomskega seminarja

Aljaž Ostrež (Author), Marjeta Kramar Fijavž (Mentor), Pavle Boškoski (Co-mentor)

Abstract

V delu diplomskega seminarja obravnavamo matrične potence in zaporedja matričnih potenc. Sprva navedemo motivacijska zgleda in naredimo pregled pojmov iz linearne algebre, potrebnih za razumevanje besedila. Nato pogledamo matrične polinome in funkcije ter navedemo nekaj osnovnih pojmov iz spektralne teorije. V osrednjem delu si ogledamo koordinatna zaporedja, asimptotsko obnašanje matričnih zaporedij in Cesàrovo konvergenco. Na koncu znanje, pridobljeno tekom diplomskega dela, uporabimo za analizo markovskih verig.

Keywords

matematika;matrike;matrične potence;markovske verige;lastne vrednosti;spektralni projektor;matrično zaporedje;Cesàrova konvergenca;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FGG - Faculty of Civil and Geodetic Engineering
Publisher:	[A. Ostrež]
UDC:	512
COBISS:	73943299
Views:	833
Downloads:	69
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Powers of matrices
Secondary abstract:	In the thesis we discuss matrix powers and sequences of matrix powers. We first give motivating examples and make an overview of the concepts from linear algebra needed to understand the text. We look at matrix polynomials and functions and list some basic concepts from spectral theory. In the central part, we look at coordinate sequences, asymptotic behavior of matrix sequences, and Cesàro summability. Finally, the knowledge gained during the thesis is used to analyze Markov chains.
Secondary keywords:	mathematics;matrices;powers of matrices;Markov chains;eigenvalues;spectral projection;matrix sequence;Cesàro summability;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	29 str.
ID:	13173875