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Lecturer(s)
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Chmelík Slavomil, PhDr. Ph.D.
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Posová Veronika, Mgr. et Mgr. Ph.D.
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Course content
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1. Vector space, axioms and basic properties 2. Vector subspace, span of a set of vectors, spanning set for a vector subspace 3. Linear dependence and independence of a family of vectors 4. Basis of a vector space, coordinates of a vector with respect to the given basis 5. Dimension of vector space, sum of subspaces, theorem on the dimension of a sum 6. Matrix algebra 7. Rank of matrix, Gaussian elimination method 8. Solving systems of linear equations using matrices, Frobenius's theorem 9. Linear maps (homomorphims) of vector spaces, coordinate matrix representations 10. Euclidean vector space, inner product, vector norm, angles between vectors 11. Ortogonal and ortonormal basis of space, Gram-Schmidt process of ortonormalization 12. Determinant of matrix, definition and basic properties, methods of computation 13. Cramer's rule, its application for solving systems of linear equations
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Learning activities and teaching methods
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Interactive lecture, Lecture with practical applications, Collaborative instruction, Lecture, Practicum
- Preparation for an examination (30-60)
- 45 hours per semester
- Preparation for formative assessments (2-20)
- 15 hours per semester
- Contact hours
- 52 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| have the knowledge specified in the "Catalog of requirements for the matriculation examination in mathematics" valid for the current school year |
| Skills |
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| apply the knowledge and skills described in the "Catalog of requirements for the matriculation examination in mathematics" valid for the current school year |
| Competences |
|---|
| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| decide whether the set of vectors forms the basis of vector space |
| apply the Gaussian elimination algorithm |
| give examples of defined concepts and their properties described in mathematical theorems |
| Skills |
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| prove the validity of simple statements in vector space |
| decide on the linear dependence or independence of a set of vectors |
| solve a system of m linear equations of n unknowns over a commutative field |
| calculate a determinant |
| Competences |
|---|
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Lecture |
| Interactive lecture |
| Practicum |
| One-to-One tutorial |
| Skills |
|---|
| Lecture |
| Practicum |
| Skills demonstration |
| One-to-One tutorial |
| Competences |
|---|
| Lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Self-study of literature |
| One-to-One tutorial |
| assessment methods |
|---|
| Knowledge |
|---|
| Combined exam |
| Test |
| Continuous assessment |
| Oral exam |
| Skills |
|---|
| Combined exam |
| Test |
| Skills demonstration during practicum |
| Continuous assessment |
| Competences |
|---|
| Combined exam |
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Recommended literature
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Bečvář, Jindřich. Lineární algebra. Praha, 2002. ISBN 80-85863-92-8.
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