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The Kroenecker Product and Vec-Operator
Karla Mercvajler (2018)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Numerical Mathematics Research Group
Cite this document...

Mercvajler, K. (2018). Kronekerov produkt i operator vektoriranje (Undergraduate thesis). 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 21 July 2019, 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 2019 July 21] 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

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)
(Numerical 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: Matematika
Study programme type: sveučilišni
Study level: preddiplomski
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 on2018-10-18 10:44:02