470-2201/01 – 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 languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesUSP, FS, FEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
ARZ0009 Ing. Vladimír Arzt
BER95 doc. Ing. Petr Beremlijski, Ph.D.
NAG0013 Ing. Judita Buchlovská Nagyová
HOR33 doc. Ing. David Horák, Ph.D.
JAH02 RNDr. Pavel Jahoda, Ph.D.
KAL0063 prof. RNDr. René Kalus, Ph.D.
KUB59 RNDr. Michael Kubesa, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
VLA04 Ing. Oldřich Vlach, Ph.D.
S1A64 RNDr. Petra Vondráková, 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: two tests, 15 points each. Conditions for credit: at least 10 points gained. Exam: written.

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:

Systems of linear algebraic equations (SLAE) Matrix calculus Linear vector spaces (LVS) Solvability of SLAE Linear mappings of LVS Linear, bilinear(, and multilinear) forms Quadratic forms Determinants Scalar product, orthogonality of vectors Orthogonal projections Spectral analysis of square matrices

Conditions for subject completion

Part-time form (validity from: 2012/2013 Winter semester, validity until: 2020/2021 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30 (30) 10
                Homework 1 Project 4  0
                Homework 2 Project 4  0
                Homework 3 Project 4  0
                Homework 4 Project 3  0
                Test Written test 15  0
        Examination Examination 70  21 3
Mandatory attendence participation: Tutorials attendance is recommended.

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Conditions for subject completion and attendance at the exercises within ISP:

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2022/2023 (B0713A060005) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0714A060016) Biomedical Technology K Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0713A060004) Design of Electrical Systems and Technologies K Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0714A060023) Communication and Information Technology K Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0714A060008) Mobile Technology P Czech Ostrava 1 Compulsory study plan
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2021/2022 (B0714A150003) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0714A150001) Control and Information Systems P Czech Ostrava 1 Compulsory study plan
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2021/2022 (B0533A110023) Applied Physics P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0713A060005) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
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2021/2022 (B0714A060012) Applied Electronics K Czech Ostrava 1 Compulsory study plan
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2020/2021 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
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2020/2021 (B0714A060008) Mobile Technology P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0714A060008) Mobile Technology K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0714A060010) Telecommunication Technology P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0714A060010) Telecommunication Technology K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0714A270002) Mechatronics K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0714A270002) Mechatronics P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0713A060007) Automotive Electronic Systems P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
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2019/2020 (B0714A060010) Telecommunication Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A150003) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0533A110023) Applied Physics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A150001) Control and Information Systems K Czech Ostrava 1 Compulsory study plan
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2019/2020 (B0713A060004) Design of Electrical Systems and Technologies K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A060010) Telecommunication Technology K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A060008) Mobile Technology K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0713A060005) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A060012) Applied Electronics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A060016) Biomedical Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0713A060005) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A060016) Biomedical Technology K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A060012) Applied Electronics K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A270002) Mechatronics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A270002) Mechatronics K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3973) Automotive Electronic Systems P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2018/2019 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2018/2019 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3973) Automotive Electronic Systems P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2013/2014 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2012/2013 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2012/2013 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
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2011/2012 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2011/2012 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2010/2011 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2010/2011 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2010/2011 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B3943) Mechatronics (3906R007) Automotive Electronics P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2023/2024 Summer
2022/2023 Summer
2021/2022 Summer
2020/2021 Summer
2019/2020 Summer
2018/2019 Summer
2017/2018 Summer
2016/2017 Summer
2015/2016 Winter
2014/2015 Winter
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