Smithova normalna oblika matrike

diplomsko delo

Aleš Pukšič (Author), Mateja Grašič (Mentor)

Abstract

V diplomskem delu je predstavljena Smithova normalna oblika kvadratne matrike z elementi iz kolobarja polinomov. Za podano kvadratno matriko izračunamo njeno Smithovo normalno obliko z uporabo elementarnih vrstičnih in stolpičnih transformacij. Za Smithovo normalno obliko matrike je značilno, da je diagonalna matrika s toliko neničelnimi elementi na diagonali, kolikšen je rang matrike, pri tem so diagonalni elementi unitarni polinomi ter prvi diagonalni element deli drugega, drugi deli tretjega in tako naprej do zadnjega neničelnega elementa na diagonali. Smithova normalna oblika matrike nam lahko služi kot orodje za ugotavljanje podobnosti matrik z elementi iz polja.

Keywords

diplomska dela;matrike;polinomi;deljivost;ekvivalentne matrike;podobne matrike;Smithova normalna oblika matrike;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[A. Pukšič]
UDC:	512.6(043.2)
COBISS:	22582792
Views:	885
Downloads:	61
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The Smith normal form of a matrix
Secondary abstract:	In this work we present the Smith normal form of a square matrix with entries from the ring of polynomials. Given a square matrix its Smith normal form can be calculated using elementary row and column transformations. The Smith normal form of the matrix with rank r is a diagonal matrix with r non-zero elements on the diagonal, diagonal elements are unitary polynomials and the first diagonal element divides the second one, the second one divides the third one and so on until the last non-zero element on diagonal. Smith normal form of a matrix can be used as a tool for checking similarity of matrices with entries from a field.
Secondary keywords:	theses;matrices;polynominals;divisibility;equivalent matrices;similar matrices;Smith normal form of a matrix;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 36 f.
ID:	9161757