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undergraduate thesis
Kroneckerov produkt matrica
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:296056
Benko, Ema
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Benko, E. (2024). Kroneckerov produkt matrica (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:296056

Benko, Ema. "Kroneckerov produkt matrica." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:296056

Benko, Ema. "Kroneckerov produkt matrica." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:296056

Benko, E. (2024). 'Kroneckerov produkt matrica', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 19 October 2024, https://urn.nsk.hr/urn:nbn:hr:126:296056

Benko E. Kroneckerov produkt matrica [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 October 19] Available at: https://urn.nsk.hr/urn:nbn:hr:126:296056

E. Benko, "Kroneckerov produkt matrica", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:296056

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Metadata
TitleKroneckerov produkt matrica
Title (english)The Kronecker Product of Matrices
AuthorEma Benko
MentorZoran Tomljanović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Numerical Mathematics
Abstract
U ovom radu bavili smo se Kroneckerovim produktom matrica. To je operacija dviju matrica koja rezultira blok-matricom. Naveli smo i dokazali osnovna svojstva ovog produkta poput množenja skalarom, transponiranja, asocijativnosti, distributivnosti slijeva i zdesna u odnosu na zbrajanje matrica. Nadalje, uveli smo novi pojam, a to je operator vektorizacije koji nam je bio važan u transformaciji Sylvesterove i Lyapunovljeve jednadžbe u jednadžbe pomoću operatora vektorizacije, gdje smo došli do pojma Kromeckerova suma. Nadalje spominjali smo i svojstvene vrijednosti Kroneckerovog produkta i Kroneckerove sume kako bismo dokazali postojanje i jedinstvenost rješenja Sylvesterove i Lyapunovljeve jednadžbe. Postoje neke metode za rješavanje tih jednadžbi.
Abstract (english)
In this work, we studied the Kronecker product of matrices. It is an operation on two matrices, resulting in a block matrix. We stated and proved the basic properties of this product, such as multiplication by a scalar, transposition, associativity, left and right distributivity with respect to matrix addition. Furthermore, we introduced a new term, named the vectorization operator, which was important in the transformation of the Sylvester and Lyapunov equations into equations using the vectorization operator. This results with the term Kronecker sum. Furthermore, we mentioned the eigenvalues of the Kronecker product and the Kronecker sum in order to prove the existence and uniqueness of the solution of the Sylvester and Lyapunov equations. We presented one method for the solution of the Sylvester and Lyapunov equations based on the vectorization operator.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:296056
Study programmeTitle: University Bachelor of Mathematics (univ. bacc. math.)
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 useLicence In copyright icon
RepositoryRepository of School of Applied Mathematics and Computer Science
Created on2024-09-12 09:25:07