Course detail
Linear Transformations and Tensor Analysis
FSI-0TAAcad. year: 2024/2025
Application of linear algebra, especially matrix calculus for describing movement in space and spatial transformations. Introduction to tensors, tensor fields and tensor analysis with an emphasis on use in physics and technical sciences.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Linear algebra in the scope of the course 1m.
Rules for evaluation and completion of the course
Aims
Study aids
Prerequisites and corequisites
Basic literature
Wasserman, Robert. Tensors and manifolds: with applications to physics. Oxford University Press, USA, 2004. (EN)
Recommended reading
Elearning
Classification of course in study plans
- Programme B-OBN-P Bachelor's 1 year of study, winter semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
1. Linear mappings. Eigenvalues and eigenvectors.
2. Diagonalizability.
3. Orthogonal transformations.
4. Unitary and Hermitian transformations.
5. Matrix decompositions: QR decomposition, LU decomposition, spectral decomposition.
6. Multilinear mappings. Tensors.
7. Symmetric and antisymmetric tensors.
9. External algebra.
8. Tensors of the 2nd order in physics.
10. Covariant derivation of vector and tensor fields.
Topics planned for 1-2 weeks.
Exercise
Teacher / Lecturer
Syllabus
Seminars follow topics of lectures. They are focused on calculations.
Elearning