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Title:
Matrične norme
Authors:
ID
Zorman, Sonja
(
Author
)
ID
Grašič, Mateja
(
Mentor
)
More about this mentor...
Files:
UN_Zorman_Sonja_2016.pdf
(376,55 KB)
MD5: 2ECE101271E57F23FD4FE57C153748C8
Language:
Slovenian
Work type:
Undergraduate thesis
Typology:
2.11 - Undergraduate Thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
V uvodnem poglavju so podane osnovne definicije in lastnosti povezane z matrikami. Predstavljene so nekatere posebne oblike matrik in pripadajoče lastnosti. Podana je tudi definicija vektorskega prostora in osnovni primeri le teh.Drugo poglavje obravnava vektorske norme. Podana je definicija vektorske norme in nekateri najbolj znani primeri.V tretjem poglavju spoznamo osrednji pojem diplomskega dela: matrično normo. Na začetku je podana definicija matrične norme in nekaj osnovnih primerov matričnih norm. Predstavljen je koncept matrične norme inducirane z vektorsko normo. Na koncu je dokazano, da je za poljubno matrično normo spektralni radij matrike manjši ali enak kot norma te matrike.
Keywords:
matrika
,
vektorski prostor
,
vektorska norma
,
matrična norma
,
spektralni radij
Place of publishing:
Maribor
Publisher:
[S. Zorman]
Year of publishing:
2016
PID:
20.500.12556/DKUM-63615
UDC:
512.6(043.2)
COBISS.SI-ID:
22756104
NUK URN:
URN:SI:UM:DK:VMNNSBJI
Publication date in DKUM:
11.11.2016
Views:
2590
Downloads:
127
Metadata:
Categories:
FNM
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Secondary language
Language:
English
Title:
Matrix norms
Abstract:
Main concept of this work are matrix norms. In the introductory chapter basic definitions and properties of matrices over a field are given. Some special forms of matrices and their basic properties are also presented. The definition of a vector space and some examples of vector spaces, needed in following chapters are given. The second chapter deals vector norms. Here the definition of a vector norm and some examples of vector norms on ${mathbb R}^n$ are given. The third chapter presents the central notion of this work: a matrix norm. First the definition of matrix norm and some examples of these are given. Next, matrix norms induced with vector norms are described. Finally it is proved that for any given matrix norm the spectral radius of the matrix is less than or equal to the norm of this matrix.
Keywords:
matrix
,
vector space
,
vector norm
,
matrix norm
,
spectral radius
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