Linear Algebra I (FSI-SLA)

Academic year 2024/2025
Supervisor: doc. Mgr. Petr Vašík, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Course type: departmental course, applied basis
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:

The course deals with the following topics: Vector spaces, matrices and operations on matrices. Consequently, determinants, matrices in a step form and the rank of a matrix, systems of linear equations. Euclidean spaces: scalar product of vectors, eigenvalues and eigenvectors, Jordan canonical form. Bilinear and quadratic forms.
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:
 
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 3 hrs. optionally                  
    Exercise  11 × 2 hrs. compulsory                  
    Computer-assisted exercise  2 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

1. Number sets, fields, operations, inversions. 
2.  Vector spaces, subspaces, homomorphisms.
3. Linear dependence of vectors, basis and dimension.
4. Transition matrices and linear mapping matrix transformation. 
5. Determinants, adjoint matrix.
6. Systems of linear equations.
7. The characteristic polynomial, eigen values, eigen vectors. 
8. Jordan normal form.
9. Unitary vector spaces.
10. Orthogonality. Gram-Schmidt process.
11. Bilinear and quadratic forms.
12. Inner, exterior and cross products – relations and applications.
13. Reserve
    Exercise

Week 1: Fundamental notions such as vectors, matrices and operations.
Following weeks: Seminar related to the topic of the lecture given in the previous week.
    Computer-assisted exercise

Seminars with computer support are organized according to current needs. They enables students to solve algorithmizable problems by computer algebra systems.
Literature - fundamental:
1.

Slovák J., Lineární algebra, Masarykova univerzita, http://www.math.muni.cz/~slovak/ftp/lectures/linearni.algebra/
2. Thomas, G. B., Finney, R.L.: Calculus and Analytic Geometry, Addison Wesley 2003.
3. Howard, A. A.: Elementary Linear Algebra, Wiley 2002.
4. Rektorys, K. a spol.: Přehled užité matematiky I., II., Prometheus 1995.
5. Searle, S. R.: Matrix Algebra Useful for Statistics, Wiley 1982.
Literature - recommended:
6. Karásek, J., Skula, L.: Algebra a geometrie, Cerm 2002.
7. Nedoma, J.: Matematika I., Cerm 2001.
8. Nedoma, J.: Matematika I., část první: Algebra a geometrie, PC-DIR 1998.
9. Horák, P., Janyška, J.: Analytická geometrie, Masarykova univerzita 1997.
10. Janyška, J., Sekaninová, A.: Analytická teorie kuželoseček a kvadrik, Masarykova univerzita 1996.
11. Mezník, I., Karásek, J., Miklíček, J.: Matematika I. pro strojní fakulty, SNTL 1992.
12. Horák, P.: Algebra a teoretická aritmetika, Masarykova univerzita 1991.
13. Procházka, L. a spol.: Algebra, Academia 1990.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-MAI-P full-time study --- no specialisation -- Cr,Ex 6 Compulsory 1 1 W
MITAI full-time study NGRI Computer Graphics and Interaction -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NADE Application Development -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NISD Information Systems and Databases -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NMAT Mathematical Methods -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NSEC Cybersecurity -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NISY do 2020/21 Intelligent Systems -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NNET Computer Networks -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NMAL Machine Learning -- Cr,Ex 6 Compulsory 1 0 W
MITAI full-time study NCPS Cyberphysical Systems -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NHPC High Performance Computing -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NVER Software Verification and Testing -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NIDE Intelligent Devices -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NISY Intelligent Systems -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NEMB do 2023/24 Embedded Systems -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NSPE Sound, Speech and Natural Language Processing -- Cr,Ex 6 Compulsory 1 0 W
MITAI full-time study NEMB Embedded Systems -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NBIO Bioinformatics and Biocomputing -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NSEN Software Engineering -- Cr,Ex 6 Elective 1 0 W
MITAI full-time study NVIZ Computer Vision -- Cr,Ex 6 Elective 1 0 W