20.500.12556/RUL-173407 Kvaternioni in kvaternionske matrike delo diplomskega seminarja Quaternions and matrices of quaternions Kvaternioni so zaradi svoje posebne strukture in lastnosti uporabno orodje v kvantni fiziki, robotiki, sodobnem računalništvu ipd. Obseg kvaternionov je primer nekomutativnega obsega, zato nas študij kvaternionskih matrik pripelje do zanimivih zaključkov. Hitro ugotovimo, da zaradi nekomutativnosti marsikatera lastnost kvaternionskih matrik, ki se na prvi pogled zdi očitna, zahteva bolj poglobljen razmislek. V delu bomo obravnavali osnovne definicije in lastnosti kvaternionov in kvaternionskih matrik ter jih primerjali s kompleksnimi matrikami. Spoznali bomo alternativno definicijo kvaternionov in njeno uporabo pri študiju lastnosti matrik, dotaknili pa se bomo tudi študija lastnih vrednosti teh matrik. Quaternions, due to their unique structure and properties, are a useful tool in quantum physics, robotics, modern computer science, and more. Quaternions are an example of a non-commutative division ring. This leads to interesting insights in the study of quaternionic matrices. A quick observation shows that, due to noncommutativity, many properties of quaternionic matrices that at first glance seem obvious actually require deeper consideration. In this work, we will examine the basic definitions and properties of quaternions and quaternionic matrices and compare them with complex matrices. We will explore an alternative definition of quaternions and its application in the study of matrix properties, and also touch upon the study of eigenvalues of these matrices. kvaternioni kvaternionske matrike lastne vrednosti kompleksna adjungirana matrika quaternions quaternionic matrices eigenvalues complex adjoint matrix true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2025-09-17 08:15:21 2025-09-17 08:15:23 2025-11-08 04:01:22 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 153724 250015235 19168.pdf 19168.pdf 1 CB9233EB03E914A7FD5EA7AE6EDD446B 17e3620a5e61748251d4554068b760d38d40576e2679f689f1e935db6562f4a7 8563044d-938d-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=217817 Fakulteta za matematiko in fiziko 0 0 0