20.500.12556/RUL-95153 Vizualizacija polarnega razcepa linearnih transformacij diplomsko delo Visualisation of polar decomposition of linear transformations V diplomskem delu obravnavamo polarni razcep za realne kvadratne matrike. Gre za produkt pozitivno definitne in ortogonalne matrike, s katerimi se tudi nekoliko podrobneje srečamo. V delu dokažemo, da polarni razcep vedno obstaja in je enolično določen za obrnljive matrike. Posebej izpeljemo ustrezne formule za ortogonalne in pozitivno definitne matrike dimenzije 2x2, prav tako pa tudi eksplicitno formulo za polarni razcep matrik dimenzije 2x2 s pomočjo katere lahko ugotovimo, kdaj ima matrika polarni razcep nad poljem racionalnih števil. Matrike si lahko predstavljamo tudi kot linearne transformacije ravnine, kar ilustriramo s slikami in interaktivnimi apleti, ki smo jih izdelali v programu GeoGebra. The thesis aims at addressing the polar decomposition of a real square matrix. This is the product of a positive-definite matrix and an orthogonal matrix that are discussed in more detail as well. It is shown and proved in the thesis that the polar decomposition always exists and it is unique for invertible matrices. The adequate formula for orthogonal and positive-definite 2x2 matrices and the explicit formula for the polar decomposition of 2x2 matrices are derived. The latter can be used to help us determine when a polar decomposition of a matrix has rational coefficients. Matrices can also be seen as linear transformations of the plane. They can be visually represented with images or interactive applets that were developed using the GeoGebra program. matrika pozitivno definitna matrika ortogonalna matrika polarni razcep linearna transformacija vizualizacija mathematics matematika true false false [E. Hrvatin] Slovenski jezik Angleški jezik Diplomsko delo/naloga 2017-09-16 02:58:58 2017-09-19 13:04:41 2025-04-17 04:53:19 0000-00-00 00:00:00 2017 0 0 42 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.643.12(043.2) 11695433 diploma.pdf diploma.pdf 1 14744F6905D3DC1FC325860AE3A7FE24 3c92515e1e10d42cb1e704cf45cac3d4653a2348091619fb8b485c01fd171797 075cb571-1aaf-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=205667 Pedagoška fakulteta 0 0 0