| Course Unit Code | 470-6501/01 |
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| Number of ECTS Credits Allocated | 10 ECTS credits |
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| Type of Course Unit * | Choice-compulsory |
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| Level of Course Unit * | Third Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Winter, Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| DOS35 | prof. RNDr. Zdeněk Dostál, DSc. |
| KOV16 | doc. Mgr. Petr Kovář, Ph.D. |
| LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |
| Summary |
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| The students will learn abaut fundamental concepts of linear algebra in the conext of applications in computer science and engineering. |
| Learning Outcomes of the Course Unit |
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| Students will learn about the role of fundamental concepts of linear algebra in analysis of engineering problems, with their properties, classification, with special matrices that appear in applications, with matrix decompositions, spectral characteristics of matrices and with matrix functions. |
| Course Contents |
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Linear mappings in elektric networks and mechanical systems.
Vector space, linear mapping and matrices.
Rank, defect, and composition of linear mappings, principle of superposition.
Matrices of linear mappings and similarity.
Bilinear and quadratic forms. Matrices and classification of bilinearr and quadratic forms, congruent matrices and LDLT decomposition.
Scalar product nad orthogonality. Norms, variational principle, the least square method and projectors.
Conjugate gradient method.
Matrix transformations and solution of linear systems.
Eigenvalues and eigenvectors, localization of eigenvalues.
Spectral decomposition of symmetric matrix. Matrix calculus, singular decomposition and pseudoinverse matrices.
Jordan form. Matrix calculus, applications..
Generalizations to infinite dimension. Banach and Hilbert spaces.
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| Recommended or Required Reading |
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| Required Reading: |
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G. Strang, Introduction to Linear Algebra, 4th Edition,
Wellesley-Cambridge Press
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Z. Dostál: Lineární algebra, VŠB-TU Ostrava 2000.
Dianne P. O'Leary, Scientific Computing with Case Studies, SIAM, Philadelphia 2009
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| Recommended Reading: |
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J. W. Demmel, Applied Numerical Linear Algebra, SIAM Philadelphia 1997.
F. R. Gantmacher: The theory of matrices. Vol. 1-2. 1959 translation. (English) |
L. Motl, M. Zahradník, Používáme lineární algebru. Karolinum, Praha 2003.
K. Výborný, M. Zahradník, Používáme lineární algebru. Karolinum, Praha 2004.
S. Míka: Numerické metody algebry, SNTL 1985. |
| Planned learning activities and teaching methods |
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| Lectures, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Examination | Examination | | |