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Title:Rang, ekvivalenca in obrnljivost matrik
Authors:ID Malič, Jasmina (Author)
ID Petek, Tatjana (Mentor) More about this mentor... New window
Files:.pdf UN_Malic_Jasmina_2016.pdf (408,71 KB)
MD5: FAF8E6E662F832E491E4A10058DB51AE
 
Language:Slovenian
Work type:Undergraduate thesis
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V diplomskem delu definiramo osnovne računske operacije z matrikami, obrnljivost matrik in prikažemo kako se izračuna inverzna matrika. Obravnavamo tudi Gaussovo eliminacijo in sisteme linearnih enačb ter ekvivalenco matrik. Dokažemo multiplikativnost determinante s pomočjo elementarnih matrik. V zadnjem poglavju pa predstavimo Shermann-Morrisonov obrazec, s katerim lahko izračunamo inverzne vrednosti določenih vsot.
Keywords:matrika, obrnljiva matrika, elementarne matrike, Gaussova eliminacija, rang, determinanta, Shermann-Morisonnov obrazec
Place of publishing:Maribor
Publisher:[J. Malič]
Year of publishing:2016
PID:20.500.12556/DKUM-59454 New window
UDC:512.6(043.2)
COBISS.SI-ID:22583304 New window
NUK URN:URN:SI:UM:DK:BVO22BJI
Publication date in DKUM:27.09.2016
Views:2284
Downloads:183
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:Rank, equivalence and invertibility of matrices
Abstract:In the thesis we define basic algebraic operations on matrices, invertibility and show how the inverse of matrix is caculated. We consider Gaussian elimination, systems of linear equations and equivalence of matrices. We prove multiplicativity of determinant using elementary matrices. Finally we present Shermann-Morrison formula which is applied for computing certain sums of matrices.
Keywords:matrix, matrix inversion, elementary matrices, Gauss elimination, rank, determinant, Shermann-Morisonn formula


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