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Methods of liear algebra and matrix operations are key building blocks of various approaches to data analysis and prediction. Their knowledge, therefore, is indispensable in research fields such as multidimensional statistics or machine learning. The course is an introduction to linear algebra and matrix theory. The goal is to present not only practical procedures to solve specific tasks, but also a more general theoretical basis, enabling the students to orient themselves is less standard problems. Theoretical explanations will be supplemented by practical examples illustrating the discussed notions and methods.
Last update: Lankaš Filip (16.04.2025)
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The course is completed by a course credit and an oral exam. The necessary condition for the course credit is an active participation in the lectures and exercises. Last update: Lankaš Filip (16.04.2025)
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Recommended:
Optional:
Last update: Lankaš Filip (16.04.2025)
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Lectures including discussion with student participation. In exercises, the students solve the given problems individually, a discussion of alternative solution methods then follows. Last update: Lankaš Filip (16.04.2025)
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1. Numbers, functions, polynomials 2. Vector space 3. Basis, dimension, subspace 4. Linear transformation 5. Matrix of a linear transformation 6. Linear equations, inverse matrices, change of basis 7. Determinant 8. Norm and inner product 9. Method of least squares 10. Operators on an inner product space 11. Eigenvalues and eigenvectors 12. Spectral theorem 13. Quadratic forms 14. Factorization of matrices Last update: Lankaš Filip (15.02.2026)
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The main study materials are lecture presentations. Last update: Lankaš Filip (16.04.2025)
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The students will acquire basic knowledge of linear algebra and matix theory. Last update: Lankaš Filip (20.05.2022)
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The main prerequisite for the course are any of the basic courses in mathematics at UCT, or equivalent knowledge. Last update: Lankaš Filip (20.05.2022)
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