Download
PDF 183.06 KB
undergraduate thesis
21   2
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
Metadata
TitleKronekerov produkt i operator vektoriranje
AuthorKarla Mercvajler
Mentor(s)Suzana Miodragović (thesis advisor)
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.
KeywordsKronecker product eigenvalues Kronecker sum vec-operator Sylvester equation Lyapunov equation
Parallel title (English)The Kroenecker Product and Vec-Operator
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Applied Mathematics
Numerical Mathematics Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Geometry and Topology
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2018-09-28
Parallel 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.
Parallel keywords (Croatian)Kroneckerov produkt svojstvene vrijednosti Kroneckerova suma operator vektorizacije Sylvesterova jednadžba Lyapunova jednadžba
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:034839