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Lecturer(s)
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Burkotová Jana, Mgr. Ph.D.
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Course content
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1. Systems of linear equations, condition number, eigenvalue and eigenvectors of matrices. 2. Matrix decompositions - LU, QR and SVD. 3. Orthogonalization and least squares method. 4. Introduction to large sparse systems of equations and their application. Direct and iterative methods. 5. Preconditioning, computer realization, termination criteria. 6. Matrix computations in statistics. 7. Special matrices in statistics, optimization and machine learning.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Understand and be able to use the methods for matrix computations.
Knowledge Gain knowledge about basic and advanced methods in matrix calculus.
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Prerequisites
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Standard knowledge from matrix calculus.
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Assessment methods and criteria
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unspecified
Colloquium: elaboration of a selected problem, defense in the form of a presentation.
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Recommended literature
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A. Björck. (2015). Numerical Methods in Matrix Computations. Springer.
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C. C. Aggarwal. (2020). Linear algebra and optimization for machine learning. Springer.
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D. Bertaccini, F. Durastante. (2018). Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications. Chapman and Hall/CRC.
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D.A. Harville. (1997). Matrix Algebra From a Statistician's Perspective. Springer.
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G. H. Golub, CH. F. Van Loan. (2013). Matrix Computations. Johns Hopkins University Press, Baltimore.
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G. Strang. (2019). Linear algebra and learning from data. Wellesley - Cambridge Press, Wellesley, MA.
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S. Puntanen, G.P.H. Styan, J. Isotalo. (2011). Matrix Tricks for Linear Statistical Models. Springer.
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