Linear algebra

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Course Unit Code470-8724/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
LUK76doc. Ing. Dalibor Lukáš, Ph.D.
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.
Learning Outcomes of the Course Unit
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.
Course Contents
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.
Recommended or Required Reading
Required Reading:
GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.
DOSTÁL, Z., VONDRÁK, V.: Lineární algebra. Elektronická skripta VŠB-TU Ostrava, http://mi21.vsb.cz
Recommended Reading:
GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.
ŠINDEL, L.: Lineární algebra v příkladech. Skripta VŠB-TU Ostrava, 1999.
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 10
        ExaminationExamination70 21