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undergraduate thesis
Kronekerov produkt i operator vektoriranje
2018. urn:nbn:hr:126:034839
Mercvajler, Karla
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Geometry and Mathematics Teaching Mathematics Research Group

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Mercvajler, K. (2018). Kronekerov produkt i operator vektoriranje (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:034839

Mercvajler, Karla. "Kronekerov produkt i operator vektoriranje." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:034839

Mercvajler, Karla. "Kronekerov produkt i operator vektoriranje." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:034839

Mercvajler, K. (2018). 'Kronekerov produkt i operator vektoriranje', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 10 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:034839

Mercvajler K. Kronekerov produkt i operator vektoriranje [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2024 December 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:034839

K. Mercvajler, "Kronekerov produkt i operator vektoriranje", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:034839

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Metadata
TitleKronekerov produkt i operator vektoriranje
Title (english)The Kroenecker Product and Vec-Operator
AuthorKarla Mercvajler
MentorSuzana Miodragović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Geometry and Mathematics Teaching Mathematics Research Group)
Osijek
Defense date and country2018-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovome radu definirati ćemo Kroneckerov produkt te navesti i dokazati njegova osnovna svojstva. Uspostaviti ćemo vezu između svojstvenih vrijednosti dviju matrica i svojstvenih vrijednosti njihovog Kroneckerovog produkta, te ćemo to primijeniti u dokazivanju svojstava za determinatnu i trag. Uvest ćemo pojam Kroneckerove sume te odrediti njezine svojstvene vrijednosti. Nadalje, baviti ćemo se operatorom vektorizacije i vidjeti njegovu povezanost sa Kroneckerovim produktom. Za kraj ćemo primjeniti Kroneckerov produkt i operator vektorizacije na rješavanje Sylvesterove i Lyapunove matrične jednadžbe.
Abstract (english)
In this paper we will define the Kronecker product, as well as specify and prove his properties. We will establish the relation between the eigenvalues of two matrices and their Kronecker product and apply it in order to prove the properties for the determinant and the trace. We will introduce the concept of the Kronecker sum and determine its eigenvalues. Furthermore, we will define the vec-operator and look at his connection with the Kronecker product. We conclude with their application to solving Sylvester and Lyapunov equations.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:034839
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
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Created on2018-10-18 10:44:02