470-2201/03 – Linear Algebra (LA1)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorprof. RNDr. René Kalus, Ph.D.Subject version guarantorprof. RNDr. René Kalus, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFS, FEI, USPIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOV74 Mgr. Tereza Kovářová, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
VLA04 Ing. Oldřich Vlach, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 8+8

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:

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.

Recommended literature:

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.

Way of continuous check of knowledge in the course of semester

Verification of study: Solution of linear systems¨and matrix algebra (max 8b) Vector spaces, linear mapping, multilinear forms (max 7b) Homeworks (15b) Conditions for credit: Minimum 10 marks of continuous assessment Written exam.

E-learning

Other requirements

No additional requirements are imposed on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Solution of systems of linear equations by elimation based methods Algebra of arithmetic vectors and matrices Inverse matrix Vector space Spaces of functions Linear mapping Bilinear and quadratic forms Determinants Eigenvalues and eigenvectors 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

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2021/2022 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21 3
Mandatory attendence participation: Participation at all seminars is obligatory, 2 absences are accepted. Participation at all lectures is strongly recommended.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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2019/2020 (B0714A060017) Biomedical Technology P English Ostrava 1 Compulsory study plan
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2018/2019 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
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2016/2017 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
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2016/2017 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
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Occurrence in special blocks

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