Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Linear Algebra 1 - NMAG113

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
Is provided by:	NMAG111
Additional information:	https://www.karlin.mff.cuni.cz/~barto/LA2425zima.html

Guarantor:	doc. Mgr. Libor Barto, 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 :	NMAG101, NMAG111
Interchangeability :	NMAG101, NMAG111
Is co-requisite for:	NMAG114
Is incompatible with:	NMAG111
Is pre-requisite for:	NMFM204
In complex pre-requisite:	NMAG201, NMAG202, NMAG206, NMAG211, NMFM202, NMSA336

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

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.

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. (20.09.2024)

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: Barto Libor, doc. Mgr., Ph.D. (20.09.2024)

Requirements to the exam -

See the website of the course.

Last update: Barto Libor, doc. Mgr., Ph.D. (20.09.2024)

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: Barto Libor, doc. Mgr., Ph.D. (20.09.2024)