Course detail
Fundamentals of Linear Algebra
FSI-TLAAcad. year: 2022/2023
The course deals with the following topics:
vector spaces, matrices and operations on matrices,
determinants, matrices in step form and rank of a matrix, systems of linear equations, Euclidean spaces, scalar product of vectors, eigenvalues and eigenvectors of a square matrix, diagonalization.
Fundamentals of analytic geometry, linear concepts
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Active attendance at the seminars.
Two 10 points semestral examps
Form of examinations: The examination has a written and an oral part. In a 120-minute written test, students solve the 4 problems
copying lecture topics.
During the oral part of the examination, the examiner goes through the test with the student. The examiner should inform the students at the last lecture about the basic rules of the examination and the evaluation of its results.
Rules for classification: The student can achieve 20 points for each problem.
Therefore he/she may achieve 100 points in total.
Final classification:
A (excellent): 90 to 100 points
B (very good): 80 to 89 points
C (good): 70 to 79 points
D (satisfactory): 60 to 69 points
E (sufficient): 50 to 59 points
F (failed): 0 to 49 points
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Jan Slovák, Martin Panák, Michal Bulant a kolektiv Matematika drsně a svižně, 1. vyd. — Brno : Masarykova univerzita, 2013 — 773 s. , Jan Slovák, Martin Panák, Michal Bulant a kolektiv ISBN 978-80-210-6307-5 (CS)
KARÁSEK, J., SKULA, L.: Lineární Algebra. Brno: AKADEMICKÉ NAKLADA-. TELSTVÍ CERM, 2005. 179 p. ISBN 80-214-3100-8. (CS)
Lang, Serge (March 9, 2004), Linear Algebra, Undergraduate Texts in Mathematics, Springer, ISBN 978-0-387-96412-6 (EN)
Recommended reading
Janyška, J., Sekaninová, A.: Analytická teorie kuželoseček a kvadrik, Masarykova univerzita 1996 (CS)
Elearning
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Determinants and their properties (volume form)
3. Systems of linear equations, row reduction and echelon forms
4. Linear dependence and independence
5. Subspaces and bases and dimensions
6. Linear transformations
7. Method of the moving frame
8. Orthogonal bases and orthogonal projections
9. Gram-Schmidt process
10. Quaternions, Spin groups
11. Eigenvalues and eigenvectors
12. Diagonalization of a matrix
13. Analytic geometry
Exercise
Teacher / Lecturer
Syllabus
Following weeks: Seminar related to the topic of the lecture given in the previous week.
Elearning