| Course Unit Code | 470-2205/03 |
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| Number of ECTS Credits Allocated | 7 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter 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 | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| BER95 | doc. Ing. Petr Beremlijski, Ph.D. |
| Summary |
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Linear algebra is one of the basic tools of formulation and solution of engineering problems. The students will get in an elementary way basic concepts and comutational skills of linear algebra, including algorithmic aspects that are important in computer implementation.
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| Learning Outcomes of the Course Unit |
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To supply working knowledge of basic concepts of linear algebra including their geometric and computational meaning, in order to enable to use these concepts in solution of basic problems of linear algebra. Student should also learn how to use the basic tools of linear algebra in applications.
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| Course Contents |
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Lectures:
An introduction to matrix calculus
Solution of systems of linear equations
Inverse matrices and LU factorization
Vector spaces and subspaces
Basis and dimension of vector spaces
Linear mapping
Bilinear and quadratic forms
Scalar product
Determinants
Eigenvalues and eigenvectors
Linear algebra applications
Exercises:
Practicing algebra of arithmetic vectors and matrices
Solution of systems of linear equations
Evaluation of inverse matrix
LU factorization
Examples of vector spaces and deduction from axioms
Evaluation of coordinates of a vector in a given basis
Examples of linear mappings and evaluation of their matrices
Matrices of bilinear and quadratic forms
Orthogonalization process
Evaluation of determinants
Evaluation of eigenvalues and eigenvectors
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| Recommended or Required Reading |
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| Required Reading: |
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| ANTON, Howard, Chris RORRES a Anton KAUL. Elementary Linear Algebra: Applications Version. 12th edition. Wiley, 2019. ISBN 978-1119666141. |
DOSTÁL, Zdeněk, Vít VONDRÁK a Dalibor LUKÁŠ. Lineární algebra [online]. VŠB-TU Ostrava, 2012 [cit. 2024-04-17]. Dostupné z: http://mi21.vsb.cz/modul/linearni-algebra
DOSTÁL, Zdeněk. Lineární algebra. Ostrava: VŠB - Technická univerzita Ostrava, 2001. ISBN 80-7078-832-1.
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| Recommended Reading: |
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STRANG, Gilbert. Linear Algebra and Its Applications. 4th edition. Brooks/Cole ISE, 2005. ISBN 978-0030105678.
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BEČVÁŘ, Jindřich. Lineární algebra. Vydání páté. Praha: Matfyzpress, 2019. ISBN 978-80-7378-378-5.
HLADÍK, Milan. Lineární algebra (nejen) pro informatiky. Praha: Matfyzpress, 2019. ISBN 978-80-7378-392-1.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| 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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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 (30) | 10 |
| Písemné práce | Written test | 24 | 10 |
| Projekt | Project | 6 | 0 |
| Examination | Examination | 70 | 21 |