20.500.12556/RUL-131038 Normalne matrike delo diplomskega seminarja Normal matrices Normalnost matrik je ena od bolj zanimivih poglavij linearne algebre. Ne samo zato, ker imajo normalne matrike razmeroma preprosto definicijo, ampak tudi zato, ker so uporabne v praksi, kar je razlog, da je bilo odkritih že $89$ karakterističnih lastnosti normalnih matrik. V tem delu smo si izbrali $25$ karakterističnih lastnosti in pokazali ekvivalence med njimi. Posvetili pa smo se tudi vprašanju, kako “blizu” sta si dve kvadratni matriki glede na njune lastne vrednosti. Ali še bolj zanimivo, kaj se zgodi z lastnimi vrednostmi matrike, če matriko malo perturbiramo. V tem delu smo na ti dve vprašanji odgovorili za normalne matrike. Matrix normality is one of the most interesting topics in linear algebra and matrix theory, since normal matrices have not only simple structures under unitary similarity but also many applications, that is why it has been done a great deal of work on them. There are $89$ different characteristic properties. In this thesis we chose $25$ of those characteristic properties and proved their equivalence to basic definition of normal matrices. We were also interested in how “close” are the matrices in terms of their eigenvalues. More interestingly, if a matrix is “perturbed” a little bit, how would the eigenvalues of the matrix change? In this thesis we present answers to these two questions if the matrices are normal. matrika lastna vrednost lastni vektor Schurjev razcep polarni razcep Hoffman-Wielandtov izrek Sunov izrek matrix eigenvalues eigenvectors Schur decomposition polar decomposition Hoffman–Wielandt theorem Sun theorem true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2021-09-22 08:15:19 2021-09-22 08:15:20 2024-05-29 13:05:01 0000-00-00 00:00:00 2021 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 120627 78322435 3758.pdf 3758.pdf 1 A835643FA210D016A8B65CDBB153EB7E 58db9b2493e2477a06735621705a73004e8f92bb0a688268d09c1115ee3c9ec1 317e4064-1b6c-11ec-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=148269 Fakulteta za matematiko in fiziko 0 0 0