470-8724/01 – Linear Algebra (LA AVAT)
Gurantor department | Department of Applied Mathematics | Credits | 4 |
Subject guarantor | doc. Ing. Dalibor Lukáš, Ph.D. | Subject version guarantor | doc. Ing. Dalibor Lukáš, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | summer |
| | Study language | Czech |
Year of introduction | 2015/2016 | Year of cancellation | 2020/2021 |
Intended for the faculties | USP | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Many engineering problems lead to solution of large-scale systems of linear equations. The aim of this course is to introduce fundamental notions of linear algebra and relate them to applications in electrical engineering. First we shall learn how to solve real and complex systems of linear equations by Gauss elimination method. The systems arises in the analysis of electrical circuits. In an intuitive manner we shall introduce notions such as base of a vector space, linear transformation and using them we will formulate basic linear problems. In the second part of the course, we shall focus on quadratic forms, which are closely related e.g. to electrical potential energy. Further we shall study orthogonality of functions, on which e.g. Fourier analysis of signals rely. Finally, we shall introduce spectral theory with applications to analysis of resonances.
Teaching methods
Lectures
Tutorials
Summary
Linear algebra is a basic tool of formulation and effective solution of technical problems. The students will get knowledge of basic concepts and computational skills of linear algebra.
Compulsory literature:
GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.
Recommended literature:
GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.
Way of continuous check of knowledge in the course of semester
2 tests (15 pts.)
Homework (15 pts.)
E-learning
Other requirements
There are no further requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Systems of linear equations.
2. Gaussian elimination.
3. Matrix calculus, inverse matrices.
4. Vector spaces.
5. Base and solvability of systems of linear equations.
6. Linear maps.
7. Bilinear forms, determinants.
8. Quadratic forms.
9. Orthogonality, orthogonal projection, the method of least squares.
10. Eigenvalues and eigenvectors.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.