SubjectsSubjects(version: 875)
Course, academic year 2019/2020
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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information:
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 > Povinné
M Bc. MMIB > 1. ročník
M Bc. MMIT > Povinné
M Bc. OM
M Bc. OM > Povinné
M Bc. OM > 1. ročník
Classification: Mathematics > Algebra
Incompatibility : NMAG101
Interchangeability : NMAG101
K//Is co-requisite for: NMAG112
XP//In complex pre-requisite: NMAG201, NMAG202, NMAG206, NMAG211, NMFM202, NMNM331, NMSA336
Annotation -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (28.05.2019)
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. RNDr. David Stanovský, Ph.D. (29.10.2019)


Literature -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (28.05.2019)

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. RNDr. David Stanovský, Ph.D. (29.10.2019)


Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (28.05.2019)
  • 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

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