Linear Algebra

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Course Unit Code470-2201/01
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, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
LUK76doc. Ing. Dalibor Lukáš, Ph.D.
JAH02RNDr. Pavel Jahoda, 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
Lectures:
Complex numbers
Solution of systems of linear equations by elimation based methods
Algebra of arithmetic vectors and matrices
Inverse matrix
Vector space
Spaces of functions
Derivation and integration of piece-wise linear functions
Linear mapping
Bilinear and quadratic forms
Determinants
Eigenvalues and eigenvectors
An introduction to analytic geometry

Exercises:
Arihmetics of complex numbers

Solution of systems of linear equations
Practicing algebra of arithmetic vectors and matrices
Evaluation of inverse matrix
Examples of vector spaces and deduction from axioms
Evaluation of coordinates of a vector in a given basis
Examples of functional spaces
Examples of linear mappings and evaluation of their matrices
Mtrices of bilinear and quadratic forms
Evaluation of determinants
Evaluation of eigenvalues and eigenvectors
Computational examples from analytic geometry
Recommended or Required Reading
Required Reading:
G. Strang, Video lectures of Linear Algebra on MIT.
R.A. Horn, C.R. Johnson, Matrix Analysis. Cambridge University Press 1990.
Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM 2003.
Z. Dostál, Lineární algebra, VŠB-TU Ostrava 2000.
G. Strang, Video lectures of Linear Algebra on MIT.
Recommended Reading:
G.H. Golub, C.F. Van Loan, Matrix Computations. The Johns Hopkins University Press 2013.
L.N. Trefethen, D. Bau. Numerical Linear Algebra. SIAM 1997.
J. Liesen, Z. Strakoš, Krylov Subspace Methods: Principles and Analysis. Oxford University Press 2012.
Z. Dostál, L. Šindel, Lineární algebra pro kombinované a distanční studium, VŠB-TU Ostrava 2003
G.H. Golub, C.F. Van Loan, Matrix Computations. The Johns Hopkins University Press 2013
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
Exercises evaluation and ExaminationCredit and Examination100 (100)51
        Exercises evaluationCredit30 (30)10
                Homework 1Project7 0
                Test 1Written test8 0
                Homework 2Project8 0
                Test 2Written test7 0
        ExaminationExamination70 21