Število različnih lastnih vrednosti simetričnih matrik

magistrsko delo

Tamara Planinšek (Author), Polona Oblak (Mentor)

Abstract

V magistrskem delu preučujemo lastne vrednosti realnih simetričnih matrik. Zanima nas najmanjše možno število $q(G)$ različnih lastnih vrednosti vseh matrik, katerih ničelno-neničelni vzorec pripada vnaprej predpisanemu grafu $G$. Za različne družine grafov $G$ izračunamo $q(G)$. Pri tem si pogledamo tudi lastnosti spojev grafov ter kartezičnih, tenzorskih in krepkih produktov grafov. V posebnem nas zanimajo grafi $G$ na $n$ točkah, za katere velja $q(G)=1,2,n-1$ ali $n$.

Keywords

inverzni problem lastnih vrednosti;lastne vrednosti;minimalni rang;simetrične matrike;graf;kvadratne forme;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.09 - Master's Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[T. Planinšek]
UDC:	512.64
COBISS:	18457689
Views:	773
Downloads:	212
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Number of distinct eigenvalues of symmetric matrices
Secondary abstract:	The aim of this work is to present the properties of eigenvalues of real symmetric matrices. We are interested in finding the minimum number of distinct eigenvalues $q(G)$ of all matrices whose zero-nonzero pattern belongs to a given graph $G$. For some families of graphs $G$ we calculate $q(G)$. We mention the properties of the join of two graphs and also Cartesian, tensor and strong products of graphs. In particular, we are interested in graphs $G$ on $n$ points, for which $q(G)=1,2, n-1$ or $n$.
Secondary keywords:	inverse eigenvalue problem;eigenvalues;minimum rank;symmetric matrices;graph;quadratic form;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages:	X, 58 str.
ID:	10962342