20.500.12556/DKUM-57266 CP - rang popolnoma pozitivne matrike CP - rang of completely positive matrix V magistrskem delu je obravnavan problem določitve cp-ranga dane popolnoma pozitivne matrike. Uvodoma so opisane osnovne lastnosti pozitivno semidefinitnih matrik in predstavljeni so konveksni stožci evklidskega prostora V. V osrednjem delu se osredotočimo na popolnoma pozitivne matrike. Matrika A je popolnoma pozitivna, če jo lahko zapišemo kot A=BB^{T} za neko nenegativno matriko B. Dokažemo osnovne lastnosti popolnoma pozitivnih matrik ter definiramo diagonalno dominantne in primerjalne matrike. Delo zaključimo z obravnavo problema določitve cp-ranga popolnoma pozitivne matrike. Obravnavamo primer za matrike manjše velikosti ter določimo zgornjo mejo za cp-rang matrike danega ranga in matrike dane velikosti. In the master thesis the problem of determining the cp-rank of a given completely positive matrix is discussed. In the introduction the basic properties of positive semidefinite matrices are described and convex cones in euclidean space V are presented. In the main part we focus on completely positive matrices. Matrix A is completely positive if it can be decomposed as A=BB^{T}, where B is a nonnegative matrix. We prove the basic properties of totally positive matrices and define diagonally dominant and comparative matrix. The thesis is concluded with a discussion of a problem of determining the cp-rank of a completely positive matrix. We consider a case of a matrix of a smaller size and set an upper bound for cp-rank matrix of a given rank and a matrix of a given order. pozitivno semidefinitna matrika popolnoma pozitivna matrika rang matrike cp-rang matrike konveksni stožec diagonalno dominantna matrika primerjalna matrika. positive semidefinite matrix completely positive matrix matrix rank cp-rank convex cones diagonally dominant matrix comparison matrix true true false [N. Jevšnik] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2016-02-05 10:27:12 2016-02-26 14:44:07 2022-06-13 03:06:55 2021-05-16 03:16:10 2015 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.643.843(043.2) 21984008 URN:SI:UM:DK:GK0OLE0U MAG_Jevsnik_Nejc_2016.pdf MAG_Jevsnik_Nejc_2016.pdf 1 65E72428A72C934F00690DACDCA17868 761d8ec71f5bc447a32da9e2dc5390b5c6ff7276d47d08ea11de861587951034 e6117c32-7c0b-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=86040 Fakulteta za naravoslovje in matematiko 0 0 0