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Invarijantni potprostori na realnim vektorskim prostorima
Martina Šarić (2016)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
Cite this document

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

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

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

Šarić, M. (2016). 'Invarijantni potprostori na realnim vektorskim prostorima', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 25 February 2020, https://urn.nsk.hr/urn:nbn:hr:126:709000

Šarić M. Invarijantni potprostori na realnim vektorskim prostorima [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2020 February 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:709000

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

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Metadata
TitleInvarijantni potprostori na realnim vektorskim prostorima
AuthorMartina Šarić
MentorIvan Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Algebra and Calculus Research Group)
Osijek
Defense date and country2016-10, 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)
Languagecroatian
URN:NBNurn:nbn:hr:126:709000
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2016-10-10 06:25:19