CP-rang popolnoma pozitivne matrike

magistrsko delo

Nejc Jevšnik (Author), Dominik Benkovič (Mentor)

Abstract

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.

Keywords

pozitivno semidefinitne matrike;popolnoma pozitivne matrike;rang matrik;cp-rang matrik;konveksni stožci;diagonalno dominantne matrike;primerjalne matrike;magistrska dela;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Jevšnik]
UDC:	512.643.843(043.2)
COBISS:	21984008
Views:	1218
Downloads:	111
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	CP - rang of completely positive matrix
Secondary abstract:	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.
Secondary keywords:	positive semidefinite matrices;completely positive matrices;matrices rank;cp-rank;convex cones;diagonally dominant matrices;comparison matrices;master theses;
URN:	URN:SI:UM:
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	51 f.
ID:	9123285