Uvod v linearni strig

magistrsko delo

Gorazd Lah (Author), Boris Zgrablić (Mentor)

Abstract

Pregledno in izčrpno je predstavljen pojem linearnega striga in osrednja vloga te linearne preslikave na področju linearne algebre. Njegova vpeljava je izvedena postopno in zložno z eksplicitno opredelitvijo s predpisom učinkovanja ter geometrijsko ponazoritvijo, najprej na realnem dvorazsežnem in trirazsežnem vektorskem prostoru geometrijskih vektorjev in nato na poljubnem končnorazsežnem vektorskem prostoru nad poljubnim poljem. Predstavljene so raznovrstne med seboj enakovredne opredelitve pojma linearni strig. Posebna pozornost je posvečena poimenovanju linearnega striga. Navedene in dokazane so temeljne lastnosti linearnih strigov na končnorazsežnem vektorskem prostoru, med katerimi je posebnega pomena ta, da linearni strigi netrivialnega končnorazsežnega vektorskega prostora razsežnosti najmanj dva generirajo njegovo posebno linearno grupo. Utemeljen je elementarni značaj linearnega striga v linearni algebri. Za vsako enoto z obsežnega seznama učbenikov s področja uvoda v linearno algebro ter teorije grup je navedeno, ali je linearni strig sploh omenjen ter v pozitivnih primerih njegova opredelitev in obravnavani rezultati.

Keywords

linearni strig;vektorski prostori;endomorfizem;linearni funkcional;Matematika;Magistrska dela;Linearna algebra;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[G. Lah]
UDC:	512.64(043.2)
COBISS:	22438152
Views:	954
Downloads:	60
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	An introduction to transvections
Secondary abstract:	The notion of transvection and its central role in linear algebra is presented transparently and comprehensively. Its introduction is performed gradually and gently with the definition through the rule of action and its geometric illustration, first on the real two- and three-dimensional vector spaces of geometric vectors, then on an arbitrary finite dimensional vector space over an arbitrary field. Miscellaneous equivalent definitions of the term transvection are given. Special attention is devoted to the denomination of transvections. Basic properties of transvections on finite dimension vector spaces are stated and their proof given, and among them of special meaning that transvections of a finite dimensional vector space of dimension at least two generate its special linear group. The elementary character of transvections in linear algebra is substantiated. An extensive list of linear algebra and group theory textbooks is examined and a report specifies for each item whether transvections are mentioned, and in positive cases the underlying definition and results.
Secondary keywords:	transvection;vector space;endomorphism;linear form;shear mapping;master theses;
URN:	URN:SI:UM:
Type (COBISS):	Master's thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	163 str.
ID:	9140595