| Course title | Linear Algebra II |
|---|---|
| Course code | UMB/585 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the summer semester. |
| Semester | Summer |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | unspecified |
| Work placements | unspecified |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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The content of the course is the theory of (abstract) vector spaces. We study properties of vector spaces and linear objects defined on vector spaces. Content of lectures: Vector spaces and subspaces, linear (in)dependence of system of vectors, generating, basis, dimension. Intersection and sum of vector subspaces. Linear map and matrix of linear map in different basis, transizion matrix and transformation of coordinates. Linear forms. Bilinear and quadratic forms. Regulatiry, signature. Sylvester's law of inertia. Spaces with skalar product. Orthogonal/orthonormal systém of vectors. Gramm-Schmidt orthogonalization. Orthogonal projectors. Eigenvectors and eigenvalues of linear transformations. Jordan canonical form. Lectures of practicals: Application of linear algebra and geometry in examples.
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
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| Learning outcomes |
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The goal of the course is (abstract) linear algebra.
Student acquires basic subjects of linear algebra useful in mathematical analysis, geometry and numerical mathematics. |
| Prerequisites |
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Knowledge of matrix computations on the level of the course UMB551 Linear Algebra.
UMB/CV010 ----- or ----- UMB/CV551 ----- or ----- UMB/010 ----- or ----- UMB/551 |
| Assessment methods and criteria |
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Combined exam, Self-reflection
Active participation in the tutorials and understanding of the theory, learning the system maxima, and passing both written and oral parts of the exam (50%). |
| 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 (2010) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Summer |