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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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1. Vector spaces, basis, dimension 2. Subspaces 3. Linear operators and matrices 4. Linear equations 5. Matrix inverse, change of basis 6. Determinant 7. Eigenvalues and eigenvectors 8. Inner product, orthogonality 9. Inner product and linear operators 10. Normal operators and matrices 11. Quadratic forms 12. Singular value decomposition 13. Applications in data analysis 14. Geometry in linear spaces Last update: Lankaš Filip (20.05.2022)
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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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