Course details

Linear Algebra

ILG Acad. year 2022/2023 Winter semester 5 credits

Current academic year

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


Course coordinator

Language of instruction

Czech, English


Credit+Examination (written)

Time span

  • 26 hrs lectures
  • 26 hrs exercises

Assessment points

  • 80 pts final exam
  • 20 pts numeric exercises




Subject specific learning outcomes and competences

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

Learning objectives

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.

Why is the course taught

Linear algebra is one of the most important branches of mathematics for engineers, regardless of their specialization, as it deals with both specific computational procedures and abstract concepts, which are useful for describing technical problems. The knowledge gained in the course is applied by graduates where engineering problems are written in  matrices, vectors and linear equations. The mastering of the basic concepts and their context will facilitate for further study and development of the chosen field.

Prerequisite knowledge and skills

Secondary school mathematics.

Study literature

  • 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
  • Hejný, M., Zaťko, V, Kršňák, P., Geometria, SPN, Bratislava, 1985
  • Kolman B., Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.
  • Kolman B., Introductory Linear Algebra, Macmillan Publ. Comp., New York 1993.
  • Havel, V., Holenda, J., Lineární algebra, STNL, Praha 1984.
  • Neri, F., Linear algebra for computational sciences and engineering, Springer, 2016.
  • Olšák, P., Úvod do algebry, zejména lineární. FEL ČVUT, Praha, 2007.
  • Kolman B., Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.

Syllabus of lectures

  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.


Syllabus of numerical exercises

Examples of tutorials are chosen to suitably complement the lectures.

Progress assessment

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

Controlled instruction

  • 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.


Exam prerequisites

The minimal total score of 8 points gained out of the mid-term exams.

Course inclusion in study plans

  • Programme BIT, 1st year of study, Compulsory
  • Programme BIT (in English), 1st year of study, Compulsory
  • Programme IT-BC-3, field BIT, 1st year of study, Compulsory
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