Invarijantni potprostori na realnim vektorskim prostorima

Šarić, Martina

undergraduate thesis

Invarijantni potprostori na realnim vektorskim prostorima

Šarić, Martina (2016)

Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group

Cite this document

APA 6th Edition

Šarić, M. (2016). Invarijantni potprostori na realnim vektorskim prostorima (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:709000

MLA 8th Edition

Šarić, Martina. "Invarijantni potprostori na realnim vektorskim prostorima." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:709000

Chicago 17th Edition

Harvard

Šarić, M. (2016). 'Invarijantni potprostori na realnim vektorskim prostorima', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 07 August 2020, https://urn.nsk.hr/urn:nbn:hr:126:709000

Vancouver

Šarić M. Invarijantni potprostori na realnim vektorskim prostorima [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2020 August 07] Available at: https://urn.nsk.hr/urn:nbn:hr:126:709000

IEEE

M. Šarić, "Invarijantni potprostori na realnim vektorskim prostorima", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:709000

Cite this item: https://urn.nsk.hr/urn:nbn:hr:126:709000

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Metadata

Title	Invarijantni potprostori na realnim vektorskim prostorima
Author	Martina Šarić
Mentor	Ivan Matić (mentor)
Granter	Josip Juraj Strossmayer University of Osijek Department of Mathematics (Chair of Pure Mathematics) (Algebra and Calculus Research Group) Osijek
Defense date and country	2016-10, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics Algebra
Abstract	U ovom završnom radu u prva tri poglavlja prisjetiti ćemo se linearnih preslikavanja na konačno dimenzionalnim vektorskim prostorima , značajnih svojstvenih vrijednosti i svojstvenih vektora operatora. Denirati ćemo invarijantne potprostore i objasniti njihovo značenje te ćemo radi lakšeg razumijevanja napraviti nekoliko primjera, a tada ćemo u četvrtom poglavlju pojasniti primjenu polinoma operatora. Matrični zapis operatora nam olakšava prikupiti informacije o njegovom djelovanju na vektorskom prostoru te nam skra- ćuje postupak pri donošenju zaključaka. Obzirom da je jedan od glavnih ciljeva linearne algebre pojednostaviti dani matrični prikaz operatora, u petom i šestom poglavlju ćemo objasniti uvjete koje zadani operator treba zadovoljavati kako bi nam bilo jasno može li se prikazati na željeni način i denirati ćemo dva specična tipa matrica koja nam uvelike doprinose pri postizanju toga cilja. U zadnjem poglavlju ćemo sve rezultate primjeniti na realne konačno dimenzionalne vektorske prostore i ispitati postojanje invarijantnih potprostora obzirom na dani operator.
Abstract (english)	In this nal work, we recall the first three chapters: linear maps on the final dimensional vector spaces, signicant eigenvalues, and eigenvectors of operators. By using a few examples to help in the explanation, we will define the invariant subspaces and explain their meaning. In chapter 4 we will explain polynomials applied to operators. The matrix form of operators helps facilitate the collection of information about its behaviour on the vector space and shortens the procedure of making conclusions. Considering that one of the main goals of linear algebra is to simplify a given matrix form of operators, in the fifth and sixth chapter we will explain the conditions that the default operator should satisfy so we can make a simplified matrix form of it. We will also define two specific matrix forms that greatly contribute in achieving this goal. In the last chapter we apply all results to the real nal dimensional vector spaces and examine the existence of invariant subspace respect to a given operator.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:126:709000
Study programme	Title: University undergraduate study programme in mathematics Study programme type: university Study level: undergraduate Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resource	Text
File origin	Born digital
Access conditions	Open access
Terms of use
Created on	2016-10-10 06:25:19