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undergraduate thesis
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Positive Definite Matrices
Jasna Okopni (2017)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Numerical Mathematics Research Group
Metadata
TitlePozitivno definitne matrice
AuthorJasna Okopni
Mentor(s)Ivana Kuzmanović (thesis advisor)
Marija Miloloža Pandur (thesis advisor)
Abstract
U radu ćemo se baviti posebnom vrstom hermitskih matrica zvanih pozitivno definitne matrice. Definirat ćemo pojmove i iskazati tvrdnje koje ćemo koristiti u daljnjem radu. Također ćemo iskazati i dokazati poznati Sylvesterov kriterij te važnu Cholesky dekompoziciju koja je učinkovita u numeričkim rješavanjima linearnih jednadžbi te ćemo pokazati koja posebna svojstva vrijede za pozitivno definitne matrice.
Keywordsmatrix positive definite matrix eigenvalues Sylvester’s criterion Cholesky decomposition
Parallel title (English)Positive Definite Matrices
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
Numerical Mathematics
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2017-09-20
Parallel abstract (English)
This paper will deal with the special type of Hermitian matrices, so called positive definite matrices. The terms and claims which are going to be used further in this paper will also be defined and stated. The well-known Sylvester’s criterion will be determined and proved as well as the important Cholesky decomposition, which is effective in numerical solving of linear equations. The special properties which are valid for positive definite matrices will also be shown.
Parallel keywords (Croatian)matrica pozitivno definitna matrica svojstvene vrijednosti Sylvesterov kriterij Cholesky dekompozicija
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:630581