Matrične norme

Lavrič, Mija (author), Slapar, Marko (mentor)

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.

• Language: Slovenian
• Keywords: vektorska norma
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Year: 2020
• PID: 20.500.12556/RUL-120109
• COBISS.SI-ID: 28289795
• Publication date in RUL: 21.09.2020

Secondary language

• Language: English
• Title: Matrix norms

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.

• Keywords: vector norm