| Course title | Linear Algebra 1 |
|---|---|
| Course code | KAG/LA1A |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | 1 |
| Semester | Winter |
| Number of ECTS credits | 7 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Algebraic structures (groupoid, group, ring, intergral domain, skew field, field) 2. Matrices, basic operations, column space, row space of matrix, rang of matrix. 3. Determinant of matrix. Application. 4. Vector space, construction, linear independence of vectors, basis, dimension, subspaces of vector space, structure of subspaces. Examples of vector spaces. 5. Homomorphisms and isomorphisms of vector spaces. 6. Scalar product in vector space: norm and angle of vetors, orthogonality of vectors and subspaces, Gramm-Schmidt method of orthogonalisation. Isometry of vector spaces. 7. Systems of linear equations, solvability, solving methods. Gauss and Jordan methods. 8. Inverse and generalised inverse (Moor-Penrose) of matrices, connection with solving of systems of linear equations. Orthogonal and idempotent matrices, connection with projections of vector spaces. 9. Eigenvalue and eigenvectors of matrices, geometric interpretation. 10. Real symmetric matrices, positive and negative (semi)definite matrices, connection with eigenvalues and traces of matrices, spectral decomposition of matrices.
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| Learning activities and teaching methods |
| unspecified |
| Learning outcomes |
| Prerequisites |
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unspecified
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| Assessment methods and criteria |
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unspecified
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| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Mathematics for Sustainable Innovation (2026) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Industrial Mathematics (2026) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Data Science (2026) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Business Mathematics (2026) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Winter |