EKSPONENTNA FUNKCIJA NA MATRIČNIH GRUPAH

Zavec, Tamara

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Title:	EKSPONENTNA FUNKCIJA NA MATRIČNIH GRUPAH
Authors:	ID Zavec, Tamara (Author) ID Pagon, Dušan (Mentor) More about this mentor...
Files:	UNI_Zavec_Tamara_2012.pdf (434,27 KB) MD5: E0930AE8C39688D177C6330C8D192270 PID: 20.500.12556/dkum/804a0d5f-26ca-4dc4-986a-859f68e15c83
Language:	Slovenian
Work type:	Undergraduate thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V diplomskem delu obravnavamo eksponentno funkcijo na matričnih grupah. Prvo poglavje je namenjeno vpeljavi grup iz matrik s kompleksnimi koeficienti. Te grupe, ki so hkrati tudi Liejeve grupe, in poznavanje njihovih lastnosti je temeljnega pomena pri vpeljavi osrednjih matematičnih struktur v diplomskem delu. Sledi konstrukcija bilinearnih form, tako na poljubnih vektorskih prostorih, kot na na matričnih grupah. Glede na njih opredelimo simplektične ter ortogonalne matrične grupe. V drugem poglavju ilustriramo geometrično strukturo na matrikah z vpeljavo pojmov metrika in norma. V nadaljevanju definiramo eksponentno funkcijo na matrikah. Seznanimo se z dvema metodama, s pomočjo katerih lahko izračunamo vrednost matrične funkcije: z metodo razvoja v potenčno vrsto in metodo diagonalizacije dane matrike. Obe metodi podkrepimo s primeri.
Keywords:	matrične grupe, bilinearne forme, ortogonalne grupe, simplektične grupe, eksponentna funkcija na matričnih grupah
Place of publishing:	Maribor
Publisher:	[T. Zavec]
Year of publishing:	2012
PID:	20.500.12556/DKUM-22348
UDC:	51(043.2)
COBISS.SI-ID:	19058184
NUK URN:	URN:SI:UM:DK:WAI3O81G
Publication date in DKUM:	06.04.2012
Views:	1977
Downloads:	159
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	EXPONENTIAL FUNCTION ON MATRIX GROUPS
Abstract:	This diploma thesis discusses exponential function on matrix groups. The first part introduces matrix groups with complex coefficients. These groups that are also Lie groups and knowledge of their characteristics are of the greatest significance by introduction of central mathematical structures in this thesis. Then a construction of bilinear forms follows, both in arbitrary vector space and in matrix groups. With regard to these we define orthogonal and symplectic groups. The second part illustrates geometric structure on matrices with introduction of the concepts of metrics and norm. In the following we define exponential function on matrix groups. We introduce two methods, by means of which we calculate the value of matrix function: by method of development in power series and method of diagonalization of given matrix. Both methods are illustrated by concrete examples.
Keywords:	matrix groups, bilinear forms, orthogonal groups, symplectic groups, exponential function on matrix groups

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