Inverzni problem lastnih vrednosti za nenegativne matrike majhnih redov

delo diplomskega seminarja

Bor Rotar (Author), Gregor Cigler (Mentor)

Abstract

Delo obravnava inverzni problem lastnih vrednosti nenegativnih matrik manjših dimenzij. Nanaša se predvsem na članek A. M. Nazarija in Sherafata z naslovom On the inverse eigenvalue problem for nonegative matrices of order two to five. Obravnavamo problem do dimenzije 5x5 s trditvami in njihovimi dokazi, hkrati pa tudi sestavimo pravila oz. pogoje s katerimi pridemo do matrik večjih dimenzij in možnih začetkov trditev za te dimenzije. Z dokazi tudi pridemo do preprostih nastavkov, če želimo iz danih lastnih vrednosti, ki upoštevajo pogoje, priti takoj do nenegativne matrike. V dokazih matrike sestavimo s trditvijo o konstrukciji, ki je tudi razložena v delu.

Keywords

matematika;nenegativni problem lastnih vrednosti matrik;konstrukcija nenegativnih matrik;matrike manjših dimenzij;spekter matrike;pridružena matrika;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[B. Rotar]
UDC:	512
COBISS:	78735619
Views:	560
Downloads:	58
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The inverse eigenvalue problem for nonnegative matrix of smaller dimensions
Secondary abstract:	The work focuses on the inverse eigenvalue problem for nonnegative matrix of smaller dimensions with its main source being a research article by A. M. Nazari and F. Sherafat titled On the inverse eigenvalue problem for nonnegative matrices of order two to five. We study the problem of dimensions for up to 5x5 with corresponding thesis and proof. Simultaneously we also try to find conditions with which we can address problems of bigger dimensions and possible sources for claims for those dimensions. With proofs we also get matrix “models” if we want to quickly find the possible nonnegative solution for the given values. We create the matrix using the newer claim of construction, that is also explained.
Secondary keywords:	mathematics;NIEP problem;inverse eigenvalue problem for nonnegative matrix;construction of nonnegative matrix;matrix of smaller dimensions;matrix spectrum;companion matrix;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	36 str.
ID:	13545846