20.500.12556/RUL-182165 Glavni koti in projektorja delo diplomskega seminarja Principal angles and projectors 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. 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. glavni koti glavni vektorji projektorji principal angles principal vectors projectors true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2026-04-26 08:15:26 2026-04-26 08:15:30 2026-04-28 12:03:01 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 159706 276629507 21388.pdf 21388.pdf 1 AE4A9B3B074A164DD8BF078D83FDEAAC b9f8be03bdff72e6d65280ec17b16ec846b4aa1817b519ebb27d6f5e60d2f826 0f86de12-4137-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233141 Fakulteta za matematiko in fiziko 0 0 0