magistrsko delo
Magdalena Gajšek (Author), Dominik Benkovič (Mentor)

Abstract

V prvem poglavju zapišemo uvod magistrskega dela. V drugem poglavju so opisani osnovni pojmi iz teorije normiranih prostorov, linearnih preslikav in matrik. V glavnem delu formuliramo Toeplitz-Hausdorffov izrek, ki pravi, da je numerični zaklad konveksna množica. Zapišemo tudi izrek o spektralni inkluziji, ki pove, da spekter operatorja leži v numeričnem zakladu. Dokažemo lastnosti numeričnega zaklada povezanih s sebiadjungiranimi in normalnimi operatorji. Nato definiramo numerični radij, podamo njegov primer in osnovne rezultate. Posebej obravnavamo numerični zaklad operatorjev (matrik) na končno dimenzionalnih vektorskih prostorih in določimo množice, ki vsebujejo numerični zaklad. Zatem so izpeljane ocene numeričnih radijev 0-1 matrik. Na koncu zapišemo posplošitve numeričnega zaklada.

Keywords

numerični zaklad;numerični radij;Hilbertov prostor;omejen linearni operator;matrike;spektri;magistrska dela;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [M. Gajšek]
UDC: 512.64(043.2)
COBISS: 20926984 Link will open in a new window
Views: 1284
Downloads: 72
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Other data

Secondary language: English
Secondary title: Numerical range
Secondary abstract: In the first chapter is written an introduction of master thesis. The second chapter describes basic concepts from the theory of normed spaces, linear mapping and matrices. In main part is formulated Toeplitz-Hausdorff theorem, which says that the numerical range is convex set. We written also theorem about spectral inclusion, which says that the spectrum of operator lies in the numerical range. We prove properties of numerical range connected with selfadjoint and normal operators. Then is defined numerical radius, his example and basic results. Specially we treat numerical range operators on finite dimensions vector spaces and we determine sets containing numerical range. After that are derived numerical radius estimates of 0-1 matrices. At the end are written generalization of numerical range.
Secondary keywords: numerical range;numerical radius;Hilbert space;bounded linear operator;matrices;spectrums;master theses;
URN: URN:SI:UM:
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 66 f.
ID: 8730964