Subjects

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Linear Algebra 1 - NMAG111

Title:	Lineární algebra 1
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2019 to 2019
Semester:	winter
E-Credits:	10
Hours per week, examination:	winter s.:4/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproMZS1920

Guarantor:	doc. RNDr. David Stanovský, Ph.D. Mgr. Dalibor Šmíd, Ph.D.
Class:	M Bc. FM M Bc. FM > Povinné M Bc. FM > 1. ročník M Bc. MMIB M Bc. MMIB > Povinné M Bc. MMIB > 1. ročník M Bc. MMIT M Bc. MMIT > Povinné M Bc. OM M Bc. OM > Povinné M Bc. OM > 1. ročník
Classification:	Mathematics > Algebra
Incompatibility :	NALG001, NMAG101
Interchangeability :	NALG001, NMAG101
Is co-requisite for:	NMAG112
Is incompatible with:	NMAG101
Is pre-requisite for:	NMFM204
Is interchangeable with:	NMAG101
In complex pre-requisite:	NMAG201, NMAG202, NMAG206, NMAG211, NMFM202, NMNM331, NMSA336

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: doc. Ing. Marek Omelka, Ph.D. (30.05.2023)

The first introductory lecture in linear algebra for General Mathematics, Financial Mathematics, and Information Security. Basic matrix operations, systems of linear equations, arithmetic vector spaces, linear dependence, linear envelope, dimension, orthogonality and orthogonalization, matrix decompositions, least squares problem, determinants.

Course completion requirements -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (25.09.2020)

See http://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproMZS1819

Literature -

Last update: doc. Mgr. Libor Barto, Ph.D. (11.10.2021)

C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM 2000.

T.S. Blyth, E.F. Robertson, Basic Linear Algebra, Springer Verlag London,2002,

S.H. Friedberg, A.J. Insel, L.E.Spence, Linear Algebra, Third Edition, Prentice-Hall, Inc., 1997

L. Barto, J. Tůma, Lineární algebra a geometrie, elektronická skripta

Requirements to the exam -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (25.09.2020)

See http://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproMZS1819

Syllabus -

Last update: doc. Mgr. Libor Barto, Ph.D. (11.10.2021)

fields, characteristic of a field,

systems of linear equations, Gauss elimination, parametric form of the solution set

elements of matrix operations, matrix as a linear mapping, group of regular matrices

abstract vector spaces, linear independence, linear span, basis, dimension, rank of a matrix, fundamental subspaces of a matrix,

linear mapping, matrix of a linear mapping, change of basis, space of linear mappings,

determinant, geometric meaning, Vandermond matrix