undergraduate thesis
Nilpotent Operators and Matrices

Nikolina Romić (2016)
Sveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Zavod za primijenjenu matematiku
Katedra za numeričku matematiku
Metadata
TitleNilpotentni operatori i matrice
AuthorNikolina Romić
Mentor(s)Darija Marković (thesis advisor)
Abstract
U radu ćemo se baviti nilpotentnim operatorima i njihovim matričnim zapisom, njihovim svojstvima te bitnim tvdnjama. Definirat ćemo pojmove koje ćemo koristiti u daljnjem radu, a to su na primjer vektorski prostor, baza i dimenzija vektorskog prostora, linearan operator, svojstvena vrijednost operatora, determinanta matrice i drugi. Zanimat će nas što je to indeks nilpotentnosti vektora, indeks nilpotentnosti operatora i koja je povezanost između njih; elementarna Jordanova klijetka te drugi pojmovi koje ćemo definirati i koristiti. Pogledat ćemo i što su Jordanovi lanci te koja je njihova veza s nilpotentnim operatorima i elementarnim Jordanovim klijetkama. Pokazat ćemo koja posebna svojstva vrijede za nilpotentne matrice i tražit ćemo primjere.
KeywordsCoset invariant subspace factoroperator nilpotent operator the height of a vector the height of a operator Jordan block the chain
Parallel title (English)Nilpotent Operators and Matrices
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za primijenjenu matematiku
Katedra za numeričku matematiku
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Algebra
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2016-09-22
Parallel abstract (English)
In this work our topic will be nilpotent operators and their matrices, their characteristics and important theorems. We will define terms that will help us in later work. Those are, for example, vector space, base and dimension of vector space, linear operator, eigenvalue, determinant and others. Our interest will be in the height of a vector, the height of a nilpotent operator and what is a connection between them; Jordan block of a nilpotent operator and other terms wich will be defined and used. Also, we shall observe the chains and their relation with nilpotent operators and Jordan blocks. We will show what special characteristics are valid for nilpotent matrices and search for some examples
Parallel keywords (Croatian)Linearna mnogostrukost invarijantan potprostor kvocijentni operator nilpotentan operator indeks nilpotentnosti vektora indeks nilpotentnosti operatora elementarna Jordanova klijetka Jordanov lanac
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:667906
CommitterMirna Šušak Lukačević