20.500.12556/DKUM-63615 Matrične norme Matrix norms V uvodnem poglavju so podane osnovne definicije in lastnosti povezane z matrikami. Predstavljene so nekatere posebne oblike matrik in pripadajoče lastnosti. Podana je tudi definicija vektorskega prostora in osnovni primeri le teh.Drugo poglavje obravnava vektorske norme. Podana je definicija vektorske norme in nekateri najbolj znani primeri.V tretjem poglavju spoznamo osrednji pojem diplomskega dela: matrično normo. Na začetku je podana definicija matrične norme in nekaj osnovnih primerov matričnih norm. Predstavljen je koncept matrične norme inducirane z vektorsko normo. Na koncu je dokazano, da je za poljubno matrično normo spektralni radij matrike manjši ali enak kot norma te matrike. Main concept of this work are matrix norms. In the introductory chapter basic definitions and properties of matrices over a field are given. Some special forms of matrices and their basic properties are also presented. The definition of a vector space and some examples of vector spaces, needed in following chapters are given. The second chapter deals vector norms. Here the definition of a vector norm and some examples of vector norms on ${mathbb R}^n$ are given. The third chapter presents the central notion of this work: a matrix norm. First the definition of matrix norm and some examples of these are given. Next, matrix norms induced with vector norms are described. Finally it is proved that for any given matrix norm the spectral radius of the matrix is less than or equal to the norm of this matrix. matrika vektorski prostor vektorska norma matrična norma spektralni radij matrix vector space vector norm matrix norm spectral radius true true false [S. Zorman] Slovenski jezik Angleški jezik Diplomsko delo 2016-09-13 21:52:20 2016-11-11 10:22:50 2022-07-03 03:06:03 2019-07-11 13:33:36 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.6(043.2) 22756104 URN:SI:UM:DK:VMNNSBJI UN_Zorman_Sonja_2016.pdf UN_Zorman_Sonja_2016.pdf 1 2ECE101271E57F23FD4FE57C153748C8 64a57f41c77a450e0d4c487f0568221d592d725cfbfe21323c907b3718fc53b4 71cfa521-7c0d-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=104203 Fakulteta za naravoslovje in matematiko 0 0 0