Popolnoma pozitiven rang simetričnih matrik

delo diplomskega seminarja

Ana Marija Kravanja (Author), Polona Oblak (Mentor)

Abstract

V delu diplomskega seminarja obravnavamo popolnoma pozitivne matrike in njihov popolnoma pozitiven rang. Dva s tem povezana problema o določanju popolne pozitivnosti matrike in izračunljivosti njenega popolnoma pozitivnega ranga sta še vedno odprta, zato sprva predstavimo glavne definicije in rezultate na temo popolnoma pozitivnih matrik. Ogledamo si povezavo med popolnoma pozitivnimi matrikami, ▫$M$▫-matrikami in diagonalno dominantnimi matrikami ter geometrijski pogled na popolnoma pozitiven rang. Nato si pogledamo alternativen postopek iskanja omejitev popolnoma pozitivnega ranga matrik s pomočjo teorije grafov. Natančneje, podamo lastnosti pripadajočih grafov, ki omejijo popolnoma pozitiven rang matrik pripadajočih vzorcev.

Keywords

popolnoma pozitivne matrike;popolnoma pozitiven rang;pozitivno semidefinitne matrike;M-matrike;konveksni stožci;pokritje grafa s klikami;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[A. M. Kravanja]
UDC:	512.643:519.17
COBISS:	58094851
Views:	916
Downloads:	120
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The completely positive rank of symmetric matrices
Secondary abstract:	In this thesis, we investigate the completely positive matrices and their completely positive rank. The problems of determining whether a matrix is completely positive and computing its completely positive rank are still open. We first present the main definitions and known results of this topic. We also present ▫$M$▫-matrices, diagonally dominant matrices, and discuss the geometric approach to complete positivity. Furthermore, we take a look at the alternative procedure of finding constraints of the completely positive rank of matrices using graph theory. In particular, we define the characteristics of the corresponding graphs which bound the completely positive rank of the matrix.
Secondary keywords:	completely positive matrices;completely positive rank;positive semidefinite matrices;M-matrices;convex cones;clique covering number;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	29 str.
ID:	12042913