Course detail

Linear Algebra

FIT-ILGAcad. year: 2022/2023

Matrices and determinants. Systems of linear equations. Vector spaces and subspaces. Linear representation, coordinate transformation. Own values and own vectors. Quadratic forms and conics.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Dana Hliněná, Ph.D.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The students will acquire an elementary knowledge of linear algebra and the ability to apply some of its basic methods in computer science.

Prerequisites

Secondary school mathematics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

  • Evaluation of the five written tests (max 20 points). 

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The students will get familiar with elementary knowledge of linear algebra, which is needed for informatics applications. Emphasis is placed on mastering the practical use of this knowledge to solve specific problems.

Specification of controlled education, way of implementation and compensation for absences

  • Participation in lectures in this course is not controlled.
  • The knowledge of students is tested at exercises  at five written tests for 4 points each and at the final exam for 80 points.
  • If a student can substantiate serious reasons for an absence from an exercise, (s)he can either attend the exercise with a different group (please inform the teacher about that) or ask his/her teacher for an alternative assignment to compensate for the lost points from the exercise.
  • The passing boundary for ECTS assessment: 50 points.

 

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Bečvář, J., Lineární algebra, matfyzpress, Praha, 2005
Bican, L., Lineární algebra, SNTL, Praha, 1979
Birkhoff, G., Mac Lane, S. Prehľad modernej algebry, Alfa, Bratislava, 1979
Havel, V., Holenda, J., Lineární algebra, STNL, Praha 1984.
Havel, V., Holenda, J., Lineární algebra, STNL, Praha 1984. (CS)
Hejný, M., Zaťko, V, Kršňák, P., Geometria, SPN, Bratislava, 1985
Kolman B., Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.
Kolman B., Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.
Kolman B., Introductory Linear Algebra, Macmillan Publ. Comp., New York 1993.
Kovár, M.,  Maticový a tenzorový počet, FEKT VUT, Brno, 2013. (CS)
Neri, F., Linear algebra for computational sciences and engineering, Springer, 2016.
Olšák, P., Úvod do algebry, zejména lineární. FEL ČVUT, Praha, 2007.

Classification of course in study plans

  • Programme BIT Bachelor's 1 year of study, winter semester, compulsory
  • Programme BIT Bachelor's 1 year of study, winter semester, compulsory

  • Programme IT-BC-3 Bachelor's

    branch BIT , 1 year of study, winter semester, compulsory

  • Programme VUB Bachelor's

    branch VU-D , 2 year of study, winter semester, elective
    branch VU-IDT , 2 year of study, winter semester, elective
    branch VU-VT , 2 year of study, winter semester, elective
    branch VU-VT , 2 year of study, winter semester, elective
    branch VU-VT , 2 year of study, winter semester, elective
    branch VU-VT , 2 year of study, winter semester, elective
    branch VU-IDT , 2 year of study, winter semester, elective
    branch VU-IDT , 2 year of study, winter semester, elective
    branch VU-IDT , 2 year of study, winter semester, elective
    branch VU-IDT , 2 year of study, winter semester, elective
    branch VU-VT , 2 year of study, winter semester, elective
    branch VU-D , 2 year of study, winter semester, elective
    branch VU-VT , 2 year of study, winter semester, elective
    branch VU-IDT , 2 year of study, winter semester, elective
    branch VU-D , 2 year of study, winter semester, elective
    branch VU-IDT , 2 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Dana Hliněná, Ph.D.
Mgr. Irena Hlavičková, Ph.D.

Syllabus

  1. Systems of linear homogeneous and non-homogeneous equations. Gaussian elimination.
  2. Matrices and matrix operations. Rank of the matrix. Frobenius theorem.
  3. The determinant of a square matrix. Inverse and adjoint matrices. The methods of computing the determinant.The Cramer's Rule.
  4. The vector space and its subspaces. The basis and the dimension. The coordinates of a vector relative to a given basis. The sum and intersection of vector spaces.
  5. The inner product. Orthonormal systems of vectors. Orthogonal projection and approximation. Gram-Schmidt orthogonalisation process.
  6. The transformation of the coordinates.
  7. Linear mappings of vector spaces. Matrices of linear transformations.
  8. Rotation, translation, symmetry and their matrices, homogeneous coordinates. 
  9. The eigenvalues and eigenvectors. The orthogonal projections onto eigenspaces.
  10. Numerical solution of systems of linear equations, iterative methods.
  11. Conic sections.
  12. Quadratic forms and their classification using sections.
  13. Quadratic forms and their classification using eigenvectors.
 

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

Mgr. Eva Sedláková
Mgr. Irena Hlavičková, Ph.D.
Mgr. Jiří Vítovec, Ph.D.
doc. RNDr. Dana Hliněná, Ph.D.
Mgr. Marie Hartmanová

Syllabus

Examples of tutorials are chosen to suitably complement the lectures.

E-learning texts

Hliněná: Slajdy z prednášok
prednaska1.pdf 0.28 MB
prednaska2.pdf 0.18 MB
prednaska3.pdf 0.36 MB
prednaska4.pdf 0.28 MB