Antisimetrične matrike

diplomska dela

Gregor Ambrož (Author), Ajda Fošner (Mentor), Dominik Benkovič (Co-mentor)

Abstract

Diplomsko delo je sestavljeno iz treh poglavij. V prvem poglavju predstavimo osnovne pojme matrik in njihove definicije. Nato podrobneje opišemo računske operacije med njimi in jih ponazorimo z zgledi. Nazadnje predstavimo determinanto matrike in njene lastnosti, lastne vrednosti in Jordanovo kanonično formo matrike. V naslednjem poglavju se posvetimo simetričnim matrikam. Najprej opišemo definicijo simetrične matrike, nato spoznamo njene osnovne lastnosti. Vsako lastnost ponazorimo z zgledom. Na koncu drugega poglavja se usmerimo tudi k definitnosti in semidefinitnosti simetričnih matrik. V uvodu tretjega poglavja predstavimo antisimetrične matrike. Nadaljujemo z osnovnimi izreki, ki jih dokažemo in ponazorimo z zgledi. V tem poglavju vpeljemo ostale izreke in definicije, ki so povezane z antisimetričnimi matrikami. Poglavje zaključimo s primerjavo simetričnih in antisimetričnih matrik, ki smo jih zasledili skozi celotno drugo in tretje poglavje diplomskega dela.

Keywords

matematika;simetrične matrike;antisimetrične matrike;definitnost;semidefinitnost;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[G. Ambrož]
UDC:	51(043.2)
COBISS:	17753608
Views:	2496
Downloads:	205
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	ANTISYMMETRIC MATRICES
Secondary abstract:	The thesis consist of three chapters. In the first chapter the basics of matrices and their definitions are presented. Arithmetic operations between them are described furthermore in greater detail and are illustrated by examples. Finally matrix's determinant and its characteristics, eigenvalues and Jordan canonical form are presented. Next chapter deals with symmetrical matrices. First the definition of symmetrical matrix is described and then its basic characteristics are recognized. Each characteristic is illustrated by an example. The end of the second chapter is directed to definite and semidefinite of the symmetrical matrices. In the introduction of the third chapter antisymmetrical matrices are presented. Basic theorems are preceded, which are proved and illustrated by examples. This chapter also introduces other theorems and definitions that are connected with antisymmetrical matrices. The chapter ends with comparisons of symmetrical and antisymmetrical matrices that were presented throughout the entire second and third chapter of the thesis.
Secondary keywords:	Symmetrical matrices;antisymmetrical matrices;definite;semidefinite.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	54 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18620