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Lecturer(s)
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Marek Josef, doc. Ing. Ph.D.
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Course content
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Week 1. Polynomials, Horner scheme, polynomial factorization Week 2. Vector space, linear dependence and independence, basis and dimension of a vector space, coordinates of a vector relative to a basis Week 3. Determinant of a matrix, definition and basic properties, determinant expansion along a row or a column Week 4. rank of a matrix, Gaussian elimination, calculation of the rank using determinants Week 5. matrix inverse, Gauss-Jordan elimination, calculation of the matrix inverse using determinants Week 6. linear map (transformation), kernel and image and their dimensions, associated matrix of a linear map and its properties Week 7. inverse linear map, linear map composition and associated matrix, vector space isomorphism, change of basis and change-of-basis matrix Week 8. systems of linear equations, homogeneous and non-homogeneous systems of equations, linear systems with an invertible matrix coefficient, Cramer's rule Week 9. eigenvalues and eigenvectors of a matrix, similarity of matrices and its properties, Jordan normal form of a matrix Week 10. inner product and its properties, norm induced by the inner product, orthogonal and orthonormal basis for a space Week 11. the Gram-Schmidt process, orthogonal projection of a vector on a subspace Week 12. method of least squares, quadratic forms and real valued symmetric matrices Week 13. inertia of a quadratic form, Sylvester's law of inertia for quadratic forms
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Learning activities and teaching methods
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Interactive lecture, Lecture with practical applications, Collaborative instruction
- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 48 hours per semester
- Preparation for formative assessments (2-20)
- 10 hours per semester
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| prerequisite |
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| Knowledge |
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| Knowledge of secondary school mathematics required. |
| learning outcomes |
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| After completing the course the student will be able to - find roots of several types of polynomials, - use the concept of a vector and a matrix, - calculate the determinant of a square matrix and to find its inverse, - solve algebraic systems of linear equations, - define and verify a vector space structure, - work with the concept of a linear map, - find eigenvalues and eigenvectors of a square matrix and to interpret them geometrically, - classify quadric surfaces, - approximate functions (data) by the method of least squares. |
| teaching methods |
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| Interactive lecture |
| Collaborative instruction |
| assessment methods |
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| Combined exam |
| Test |
| Skills demonstration during practicum |
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Recommended literature
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Havel, Václav; Holenda, Jiří. Lineární algebra. 1. vyd. Praha : SNTL, 1984.
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Holenda, Jiří. Lineární algebra. 2. vyd. Plzeň : Západočeská univerzita, 1992. ISBN 80-7082-075-6.
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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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