Glavni koti in projektorja : delo diplomskega seminarja

Babič, Amanda (author), Plevnik, Lucijan (mentor)

V diplomskem delu obravnavamo projektorje v kompleksnem prostoru in glavne kote med podprostori ter pripadajoče glavne vektorje, skupaj z njihovimi lastnostmi in medsebojnimi povezavami. Ključnega pomena sta Halmosov in Wedinov izrek, ki preko glavnih kotov omogočata kanonično razčlenitev para projektorjev. Na podlagi tega analiziramo lastnosti vsote, razlike in produkta dveh projektorjev. Posebej obravnavamo vprašanje, kdaj lahko dano hermitsko matriko zapišemo kot vsoto ali razliko dveh projektorjev. Pri produktu pa pokažemo, da so njegove singularne vrednosti tesno povezane z glavnimi koti.

• Language: Slovenian
• Keywords: glavni koti, glavni vektorji, projektorji
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2026
• PID: 20.500.12556/RUL-182165
• UDC: 512
• COBISS.SI-ID: 276629507
• Publication date in RUL: 26.04.2026

Secondary language

• Language: English
• Title: Principal angles and projectors

Abstract

In this thesis we study projectors in a complex space and the principal angles between subspaces together with the corresponding principal vectors, as well as their properties and mutual relationships. The Halmos and Wedin theorems play a key role, as they provide a canonical decomposition of a pair of projectors with respect to the principal angles. Using this decomposition, we analyze the properties of the sum, difference, and product of two projectors. We also consider the question of when a given Hermitian matrix can be expressed as the sum or difference of two projectors. For the product, it turns out that the singular values of the product are closely related to the principal angles.

• Keywords: principal angles, principal vectors, projectors