Course detail
Linear Algebra I
FSI-SLAAcad. year: 2025/2026
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Form of examinations: The exam is written and has two parts.
The exercises part takes 100 minutes and 6 exercises are given to solve.
The theoretical part takes 20 minutes and 6 questions are asked.
At least 50% of the correct results must be obtained from each part. If less is met in one of the parts, then the classification is F (failed).
Exercises are evaluated by 3 points, questions by 1 point.
If 50% of each part is met, the total classification is given by the sum.
A (excellent): 22 - 24 points
B (very good): 20 - 21 points
C (good): 17 - 19 points
D (satisfactory): 15 - 16 points
E (enough): 12 - 14 points
F (failed): 0 - 11 points
Attendance at lectures is recommended, attendance at seminars is required. The lessons are planned on the basis of a weekly schedule. The way of compensation for an absence is in the competence of the teacher.
Aims
thinking.
Students will be made familiar with algebraic operations,linear algebra, vector and Euclidean spaces, and analytic geometry. They will be able to work with matrix operations, solve systems of linear equations and apply the methods of linear algebra to analytic geometry and engineering tasks. When completing the course, the students will be prepared for further study of mathematical and technical disciplines.
Study aids
Prerequisites and corequisites
Basic literature
Slovák J., Lineární algebra, Masarykova univerzita, http://www.math.muni.cz/~slovak/ftp/lectures/linearni.algebra/ (CS)
Rektorys, K. a spol.: Přehled užité matematiky I., II., Prometheus 1995.
Searle, S. R.: Matrix Algebra Useful for Statistics, Wiley 1982.
Thomas, G. B., Finney, R.L.: Calculus and Analytic Geometry, Addison Wesley 2003.
Recommended reading
Horák, P., Janyška, J.: Analytická geometrie, Masarykova univerzita 1997.
Janyška, J., Sekaninová, A.: Analytická teorie kuželoseček a kvadrik, Masarykova univerzita 1996.
Karásek, J., Skula, L.: Algebra a geometrie, Cerm 2002.
Mezník, I., Karásek, J., Miklíček, J.: Matematika I. pro strojní fakulty, SNTL 1992.
Nedoma, J.: Matematika I., Cerm 2001.
Nedoma, J.: Matematika I., část první: Algebra a geometrie, PC-DIR 1998.
Procházka, L. a spol.: Algebra, Academia 1990.
Classification of course in study plans
- Programme B-MAI-P Bachelor's 1 year of study, winter semester, compulsory
- Programme MITAI Master's
specialization NSEC , 0 year of study, winter semester, elective
specialization NISY up to 2020/21 , 0 year of study, winter semester, elective
specialization NNET , 0 year of study, winter semester, elective
specialization NMAL , 0 year of study, winter semester, compulsory
specialization NCPS , 0 year of study, winter semester, elective
specialization NHPC , 0 year of study, winter semester, elective
specialization NVER , 0 year of study, winter semester, elective
specialization NIDE , 0 year of study, winter semester, elective
specialization NISY , 0 year of study, winter semester, elective
specialization NEMB , 0 year of study, winter semester, elective
specialization NSPE , 0 year of study, winter semester, compulsory
specialization NEMB , 0 year of study, winter semester, elective
specialization NBIO , 0 year of study, winter semester, elective
specialization NSEN , 0 year of study, winter semester, elective
specialization NVIZ , 0 year of study, winter semester, elective
specialization NGRI , 0 year of study, winter semester, elective
specialization NADE , 0 year of study, winter semester, elective
specialization NISD , 0 year of study, winter semester, elective
specialization NMAT , 0 year of study, winter semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
Seminars with computer support are organized according to current needs. They enables students to solve algorithmizable problems by computer algebra systems.