Numerička slika operatora i matrica

master's thesis

• Title (english): Numerical image of the operator and matrix
• Author: Petar Matić
• Mentor: Tomislav Berić (mentor)
• Committee member: Tomislav Berić (predsjednik povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu smo razvili osnovnu teoriju numeričke slike i pokazali neka fundamentalna svojstva koja vrijede za numeričku sliku i numerički radijus. Radili smo s ograničenim linearnim operatorima nad kompleksnim Hilbertovim prostorima. Opisali smo numeričku sliku raznih linearnih operatora, posebno za hermitske i normalne operatore. Pokazano je kako su povezani numerička slika i spektar operatora. Promatrali smo što se može zaključiti o numeričkoj slici ako nam je dan linearni operator i, obratno, ako nam je dana numerička slika nekog operatora, pokazali smo što se može zaključiti o tom istom operatoru iz njegove numeričke slike.

Abstract (english)

In this thesis, we have developed the basic theory of numerical range and shown some fundamental properties that apply to numerical range and numerical radius. We worked with bounded linear operators over complex Hilbert spaces. We have described the numerical range of various linear operators, especially for self-adjoint and normal operators. It was shown how the numerical range and the spectrum are related. We observed what can be concluded about the numerical range if we are given a linear operator and, conversely, if we are given the numerical range of an operator, we have shown what can be concluded about that same operator from its numerical range.

• Keywords: numerička slika; numerički radijus; kompleksni Hilbertovi prostori; linearni operatori
• Keywords (english): numerical range; numerical radius; complex Hilbert spaces; linear operators
• Language: croatian
• URN:NBN: urn:nbn:hr:217:493031
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-03-01 13:01:50