Moore-Penroseov matrični inverz

diplomsko delo

Karmen Koznicov (Author), Dominik Benkovič (Mentor)

Abstract

V uvodu predstavimo posamezna poglavja diplomskega dela. V drugem poglavju podamo definicije in opišemo vrste matrik ter operacije, ki jih opravljamo na matrikah. Definiramo rang matrike, transponiranje in Gauss-Jordanovo eliminacijsko metodo, ki jo bomo potrebovali pri izračunu Moore-Penroseovega inverza. V tretjem poglavju predstavimo Moore-Penroseov inverz poljubne matrike in zapišemo njegove lastnosti. Zadnje poglavje je namenjeno izračunu Moore-Penroseovega inverza. Predstavimo tri algoritme, s katerimi lahko izračunamo Moore-Penroseov inverz. Opišemo njihovo računsko zahtevnost in jih predstavimo na primeru.

Keywords

matrika;rang matrike;inverzna matrika;Gauss-Jordanova eliminacijska metoda;Moore-Penroseov inverz;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[K. Koznicov]
UDC:	512.643:519.17(043.2)
COBISS:	22583048
Views:	1275
Downloads:	123
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Moore-penrose matrix inverse
Secondary abstract:	In the introduction each chapter of the graduation thesis is presented. In the second chapter we give definitions and descriptions of the types of matrices and operations that are performed with them. We define the rank of a matrix, the transpose of a matrix, and the Gauss-Jordan elimination method, which will be needed in the calculation of the Moore-Penrose inverse. In the third chapter we present the Moore-Penrose inverse of a matrix and its characteristics. The last chapter deals with the calculation of the Moore-Penrose inverse. We present three algorithms, which can be used to calculate the Moore-Penrose inverse. We describe their computational complexity and present them through examples.
Secondary keywords:	matrix;rank of a matrix;inversion matrix;Gauss-Jordan elimination method;Moore-Penrose inverse;theses;Univerzitetna in visokošolska dela;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	50 f.
ID:	9162011