Reševanje matričnih enačb

diplomsko delo

Metka Markoč (Author), Dušan Pagon (Mentor)

Abstract

Diplomsko delo obravnava reševanje linearnih matričnih enačb in zajema štiri poglavja. V prvem so definirani pojmi in osnovne lastnosti, s katerimi se operira v nadaljevanju. V drugem poglavju je govora o Kroneckerjevem produktu in Kroneckerjevi vsoti, dveh osnovnih operacijah, ki se uporabljata pri drugačni, velikokrat ugodnejši obliki zapisa matričnih enačb. V tretjem poglavju je opisano še eno pomembno orodje, uporabno pri reševanju matričnih enačb, to je Moore-Penroseov psevdoinverz. Zadnje poglavje je namenjeno predstavitvi relacij med danimi matrikami, ki zagotavljajo obstoj rešitev štirih obravnavanih tipov enačb. S preprostimi pogoji se torej pri vsakem posameznem tipu enačbe lahko nemudoma ugotovi, ali je rešitev enačbe sploh smiselno iskati, pri eni izmed enačb je podana tudi oblika rešitve.

Keywords

matematika;matrične enačbe;Kroneckerjev produkt;Kroneckerjeva enačba;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:	[M. Markoč]
UDC:	51(043.2)
COBISS:	17689352
Views:	4964
Downloads:	516
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	SOLVING MATRIX EQUATIONS
Secondary abstract:	The thesis deals with solving linear matrix equations and includes four chapters. In the first chapter terms and basic properties are defined, which are used in followed text. The second chapter refers to a Kronecker product and Kronecker sum. Those are two basic operations, which are used to give a convenient representation for linear matrix equations. In the third chapter another important tool, useful in solving matrix equations is described. This is the Moore-Penrose pseudoinverse. The final chapter deals with relations between coefficients of a linear matrix equation, which provide solutions for four concrete types of matrix equations. With simple conditions for each type of the concerned matrix equations we can efficiently check the existence of its solutions. For one of these types of equations the exact form of the solution is also described.
Secondary keywords:	Kronecker product;Kronecker sum;matrix equation;Moore-Penrose pseudoinverse;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	29 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18537