Course details

# Linear Algebra

ILG Acad. year 2020/2021 Winter semester 5 credits

Guarantor

Deputy Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Instructor

Hliněná Dana, doc. RNDr., Ph.D. (DMAT FEEC BUT)

Svoboda Zdeněk, RNDr., CSc. (DMAT FEEC BUT)

Vítovec Jiří, Mgr., Ph.D. (DMAT FEEC BUT)

Subject specific learning outcomes and competences

Learning objectives

Why is the course taught

Prerequisite kwnowledge and skills

Study literature

- Bečvář, J., Lineární algebra, matfyzpress, Praha, 2005. (in Czech).
- Kovár, M., Maticový a tenzorový počet, FEKT VUT, Brno, 2013. (in Czech).
- Olšák, P., Úvod do algebry, zejména lineární. FEL ČVUT, Praha, 2007. (in Czech).

Fundamental literature

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

Syllabus of lectures

- Systems of linear homogeneous and non-homogeneous equations. Gaussian elimination.
- Matrices and matrix operations. Rank of the matrix. Frobenius theorem.
- The
*determinant*of a square matrix. Inverse and adjoint matrices. The methods of computing the determinant.The Cramer's Rule. - 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.
- The inner product. Orthonormal systems of vectors. Orthogonal projection and approximation. Gram-Schmidt orthogonalisation process.
- The transformation of the coordinates.
- Linear mappings of vector spaces. Matrices of linear transformations.
- Rotation, translation, symmetry and their matrices, homogeneous coordinates.
- The eigenvalues and eigenvectors. The orthogonal projections onto eigenspaces.
- Numerical solution of systems of linear equations, iterative methods.
- Conic sections.
- Quadratic forms and their classification using sections.
- Quadratic forms and their classification using eigenvectors.

Syllabus of numerical exercises

Progress assessment

- Evaluation of two homework assignments - groupwork (max 10 points).
- Evaluation of the two mid-term exams (max 30 points).

Controlled instruction

- Participation in lectures in this course is not controlled.
- The knowledge of students is tested at exercises; including two homework assignments worth for 5 points each, at two midterm exams for 15 points each, and at the final exam for 60 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

Course inclusion in study plans