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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 2024
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
Additional information:	https://www.karlin.mff.cuni.cz/~barto/LA2425zima.html

Guarantor:	doc. Mgr. Libor Barto, Ph.D.
Teacher(s):	doc. Mgr. Libor Barto, Ph.D. Mgr. Jan Blechta, Ph.D. Bc. Filip Filipi Mgr. Kateřina Fuková Bc. Simona Hlavinková RNDr. Jaroslav Hron, Ph.D. Mgr. Maryia Kapytka Bc. Jakub Knesel Mgr. Daniel Komárek RNDr. Alexander Slávik, 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, NMAG113
Interchangeability :	NALG001, NMAG101
Is co-requisite for:	NMAG112
Is incompatible with:	NMAG101, NMAG113
Is interchangeable with:	NMAG113, NMAG101
In complex pre-requisite:	NMAG201, NMAG202, NMAG206, NMAG211, NMFM202, NMNM331, NMSA336

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Annotation -

The first introductory lecture in linear algebra for General 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.

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

Course completion requirements -

See the website of the course.

Last update: Barto Libor, doc. Mgr., Ph.D. (18.09.2024)

Literature -

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

Last update: Šťovíček Jan, doc. RNDr., Ph.D. (01.10.2023)

Requirements to the exam -

See the website of the course.

Last update: Barto Libor, doc. Mgr., Ph.D. (18.09.2024)

Syllabus -

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

Last update: Stanovský David, doc. RNDr., Ph.D. (30.09.2022)