Course detail
Linear Transformations and Tensor Analysis
FSI-0TA Acad. year: 2024/2025 Winter semester
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
Czech
Number of ECTS credits
3
Supervisor
Department
Entry knowledge
Linear algebra in the scope of the course 1m.
Rules for evaluation and completion of the course
Exam: both written and oral.
Aims
The student will learn to effectively use the tools of linear algebra, especially matrix calculus for describing movement in space and spatial transformations. He will use this knowledge especially in various tasks of mechanics. The student will also learn to work with tensors and tensor fields.
Study aids
Supplementation of direct teaching in the form of e-learning support will be continuously used.
The study programmes with the given course
Programme B-OBN-P: Common Offer, Bachelor's, elective
Type of course unit
Lecture
26 hours, optionally
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
13 hours, compulsory
Syllabus
Seminars follow topics of lectures. They are focused on calculations.