Course details

# Linear Algebra

SLA FME BUT SLA Acad. year 2019/2020 Winter semester 6 credits

Algebraic operations: groups, vector spaces, matrices and operations on matrices.

Fundamentals of linear algebra: determinants, matrices in step form and rank of a matrix, systems of linear equations. Euclidean spaces: scalar product of vectors, eigenvalues and eigenvectors. Fundamentals of analytic geometry: linear concepts, conics, quadrics.

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Subject specific learning outcomes and competences

Learning objectives

Prerequisite kwnowledge and skills

Study literature

- Thomas, G. B., Finney, R.L.: Calculus and Analytic Geometry, Addison Wesley 2003.
- Howard, A. A.: Elementary Linear Algebra, Wiley 2002.
- Rektorys, K. a spol.: Přehled užité matematiky I., II., Prometheus 1995. (in Czech)
- Nicholson, W. K.: Elementary Linear Algebra with Applications, PWS 1990.
- Searle, S. R.: Matrix Algebra Useful for Statistics, Wiley 1982.
- Karásek, J., Skula, L.: Algebra a geometrie, Cerm 2002. (in Czech)
- Nedoma, J.: Matematika I., Cerm 2001. (in Czech)
- Nedoma, J.: Matematika I., část první: Algebra a geometrie, PC-DIR 1998. (in Czech)
- Horák, P., Janyška, J.: Analytická geometrie, Masarykova univerzita 1997. (in Czech)
- Janyška, J., Sekaninová, A.: Analytická teorie kuželoseček a kvadrik, Masarykova univerzita 1996.(in Czech)
- Mezník, I., Karásek, J., Miklíček, J.: Matematika I. pro strojní fakulty, SNTL 1992. (in Czech)
- Horák, P.: Algebra a teoretická aritmetika, Masarykova univerzita 1991. (in Czech)
- Procházka, L. a spol.: Algebra, Academia 1990. (in Czech)
- Gilbert Strang: Introduction to Linear Algebra, Fifth Edition. Wellesley-Cambridge Press; Fifth Edition edition (June 10, 2016). ISBN-13: 978-0980232776.

Syllabus of lectures

2. week. Vector spaces, subspaces, homomorphisms. The linear dependence of vectors, the basis and dimension..

3. week. Matrices and determinants.

4. week. Systems of linear equations.

5. week. The characteristic polynomial, Eugen values, Eugen vectors. Jordan normal form.

6. week. Dual vector spaces. Linear forms.

7. week. Bilinear and quadratic forms.

8. week. Unitary spaces. Schwarz inequality. Orthogonality.

9. week. Inner, exterior, cross and triple products - relations and applications.

10. week. Symplectic spaces.

11. week. Affine and Euclidean spaces. Geometry of linear objects.

12. week. Projective spaces.

13. week. Geometry of conics and quadrics.

Syllabus of numerical exercises

Following weeks: Seminar related to the topic of the lecture given in the previous week.

Syllabus of computer exercises

Progress assessment

Form of examinations: The examination has a written and an oral part. In a 120-minute written test, students

solve the following 5 problems.

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: Student can achieve 4 points for each problem. Therefore, the students may achieve 20 points in total.

Final classification: A (excellent): 19 to 20 points

B (very good): 17 to 18 points

C (good): 15 to 16 points

D (satisfactory): 13 to 14 points

E (sufficient): 10 to 12 points

F (failed): 0 to 9 points

Controlled instruction

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Schedule

Course inclusion in study plans