Linear Algebra 1 - NMAG113
Title: Lineární algebra 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
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
Is provided by: NMAG111
Additional information: https://www.karlin.mff.cuni.cz/~stovicek/index.php/cs/2324zs-nmag111
Guarantor: doc. RNDr. Jan Šťovíček, 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
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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: Šťovíček Jan, doc. RNDr., Ph.D. (01.10.2023)
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: Šťovíček Jan, doc. RNDr., Ph.D. (01.10.2023)
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: Omelka Marek, doc. Ing., Ph.D. (30.05.2023)