Matrične norme

diplomsko delo

Mija Lavrič (Author), Marko Slapar (Mentor)

Abstract

V diplomskem delu obravnavamo matrične norme na algebri M_n kvadratnih n×n kompleksnih matrik. Matrične norme so vektorke norme na M_n, za katere dodatno predpostavimo submultiplikativnost. Posebno pozornost namenimo operatorskim normam, ki so inducirane z vektorskimi normami na C^n. Obravnavamo tudi spektralni radij matrik in pokažemo, da je spektralni radij največja spodnja meja za vrednosti vseh matričnih norm matrike.

Keywords

številske vrste;funkcijske vrste;enakomerna konvergenca;potenčne vrste;trigonometrične funkcije;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Lavrič]
UDC:	512.643.3(043.2)
COBISS:	28289795
Views:	1291
Downloads:	162
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Matrix norms
Secondary abstract:	In this diploma thesis we study matrix norms on the algebra M_n of square n×n complex matrices. Matrix norms are vector norms on M_nthat are also submultiplicative. We especially focus on operator norms that are induced by vector norms on C^n. We also introduce the spectral radius of a matrix and show that the spectral radius of a matrix is the greatest lower bound for the values of all matrix norms of the matrix.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj: Fizika-matematika
Pages:	20 str.
ID:	12023601