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Lecturer(s)
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Šedivá Blanka, RNDr. Ph.D.
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Kaiser Jan
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Kaiser Tomáš, Prof. RNDr. DSc.
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Holub Přemysl, Doc. RNDr. Ph.D.
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Šebková Milena, RNDr.
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Ekstein Jan, RNDr. Ph.D.
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Čada Roman, Doc. Ing. Ph.D.
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Teska Jakub, RNDr. Mgr. Ph.D.
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Kabela Adam, RNDr. Ph.D.
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Course content
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Week 1: Vectors, inner and vector product, vector algebra in 2D and 3D, mutual location of geometrical units. Week2: Metrical exercises from vector algebra, transversal and distance of non-intersecting lines. Quadratic faces. Week3: Polynomials, polynomial factorization, partial fractions. Week4: Matrix operations and determinants. Week5: Vector space, basis and dimension of a vector space, coordinates of a vector relative to a basis. Week6: Rank of a matrix, matrix inverse. Week7: Linear map (transformation): kernel and image and their dimension. Week8: Linear map (transformation): associated matrix of a linear map, change of basis. Week9: Systems of linear equations. Week10: Eigenvalues and eigenvectors of a matrix, Jordan normal form of a matrix. Week11: Inner product, orthogonal and orthonormal basis for a space (the Gram-Schmidt process), orthogonal projection of a vector on a subspace, method of least squares. Week12: Quadratic forms, inertia of a quadratic form. Week13: Written exam.
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Learning activities and teaching methods
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Skills demonstration, Individual study
- Contact hours
- 26 hours per semester
- Undergraduate study programme term essay (20-40)
- 26 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| vymezit pojem polynomu |
| vymezit pojem vektoru |
| poznat rovnice základních geometrických útvarů |
| Skills |
|---|
| použít základy analytické geometrie |
| vyřešit jednoduché soustavy rovnic |
| Competences |
|---|
| N/A |
| N/A |
| learning outcomes |
|---|
| Knowledge |
|---|
| vysvětlit pojem vektoru, matice, polynomu |
| popsat pojem lineárního prostoru a lineárního zobrazení |
| charakterizovat vlastní čísla a vlastní vektory |
| Skills |
|---|
| určit kořeny polynomu |
| vypočítat determinant matice, matici inverzní a hodnost matice |
| vyřešit soustavu algebraických rovnic |
| určit vlastní čísla a vlastní vektory matice |
| použít metodu nejmenších čtverců |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Seminar |
| Skills demonstration |
| Individual study |
| Skills |
|---|
| Seminar |
| Individual study |
| Competences |
|---|
| Seminar |
| Individual study |
| assessment methods |
|---|
| Knowledge |
|---|
| Skills demonstration during practicum |
| Seminar work |
| Skills |
|---|
| Seminar work |
| Competences |
|---|
| Seminar work |
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Recommended literature
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Tesková, Libuše. Lineární algebra. 1. vyd. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-797-1.
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Tesková, Libuše. Sbírka příkladů z lineární algebry. 5. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7043-263-2.
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