Linearni operatori na unitarnim prostorima

master's thesis

• Title (english): Linear operaters on inner product spaces
• Author: Marta Štriga
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Veronika Pedić Tomić (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Committee member: Goran Igaly (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-07-19, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu proučavamo linearne operatore na unitarnim prostorima. Jedno od vaćnih pitanja koje razmatramo su matrični zapisi linearnih operatora u ortonormiranoj bazi, odnosno paru ortonormiranih baza. U ovom razmatranju se pojavljuju određene klase linearnih operatora karakteristične samo za unitarne prostore, a to su hermitski, normalni i unitarni operatori. Dokazat ćemo spektralni teorem, te proučiti polarnu formu operatora i dekompoziciju singularnim vrijednostima.

Abstract (english)

In this thesis, we study linear operators on inner-product spaces. One of the important issues we discuss are matrix representations of linear operators with respect to an orthonormal basis or a pair of orthonormal bases. In this consideration, certain classes of linear operators on inner-product spaces appear, and these are selfadjoint, normal and unitary operators. We prove the spectral theorem, the polar form of an operator and the singular value decomposition.

• Keywords: matrični zapisi linearnih operatora; ortonormirana baza; spektralni teorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:540983
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-07-24 14:05:54