# 470-2201/03 – Linear Algebra (LA1)

 Gurantor department Department of Applied Mathematics Credits 4 Subject guarantor prof. RNDr. René Kalus, Ph.D. Subject version guarantor prof. RNDr. René Kalus, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2015/2016 Year of cancellation Intended for the faculties FEI, FS, USP Intended for study types Bachelor
Instruction secured by
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.

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.

### 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

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (B0714A060017) Biomedical Technology P English Ostrava 1 Compulsory study plan
2024/2025 (B0714A060019) Biomedical Assistive Technology P English Ostrava 1 Compulsory study plan
2024/2025 (B0714A060020) Electrical Engineering P English Ostrava 1 Compulsory study plan
2024/2025 (B0714A150002) Control and Information Systems P English Ostrava 1 Compulsory study plan
2023/2024 (B0714A060020) Electrical Engineering P English Ostrava 1 Compulsory study plan
2023/2024 (B0714A150002) Control and Information Systems P English Ostrava 1 Compulsory study plan
2023/2024 (B0714A060017) Biomedical Technology P English Ostrava 1 Compulsory study plan
2023/2024 (B0714A060019) Biomedical Assistive Technology P English Ostrava 1 Compulsory study plan
2022/2023 (B0714A060017) Biomedical Technology P English Ostrava 1 Compulsory study plan
2022/2023 (B0714A060017) Biomedical Technology K English Ostrava 1 Compulsory study plan
2022/2023 (B0714A060019) Biomedical Assistive Technology P English Ostrava 1 Compulsory study plan
2022/2023 (B0714A150002) Control and Information Systems P English Ostrava 1 Compulsory study plan
2022/2023 (B0714A150004) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2022/2023 (B0714A060020) Electrical Engineering P English Ostrava 1 Compulsory study plan
2021/2022 (B0714A060017) Biomedical Technology P English Ostrava 1 Compulsory study plan
2021/2022 (B0714A060017) Biomedical Technology K English Ostrava 1 Compulsory study plan
2021/2022 (B0714A060019) Biomedical Assistive Technology P English Ostrava 1 Compulsory study plan
2021/2022 (B0714A060020) Electrical Engineering P English Ostrava 1 Compulsory study plan
2021/2022 (B0714A150004) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2021/2022 (B0714A150002) Control and Information Systems P English Ostrava 1 Compulsory study plan
2021/2022 (B0713A060006) Electrical Power Engineering P English Ostrava 1 Compulsory study plan
2021/2022 (B0714A060013) Applied Electronics P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A150002) Control and Information Systems P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A150004) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A060017) Biomedical Technology K English Ostrava 1 Compulsory study plan
2020/2021 (B0714A060017) Biomedical Technology P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A060019) Biomedical Assistive Technology P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A060013) Applied Electronics P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A060009) Mobile Technology P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A060011) Telecommunication Technology P English Ostrava 1 Compulsory study plan
2020/2021 (B0713A060006) Electrical Power Engineering P English Ostrava 1 Compulsory study plan
2020/2021 (B0713A060008) Automotive Electronic Systems P English Ostrava 1 Compulsory study plan
2020/2021 (B0714A060020) Electrical Engineering P English Ostrava 1 Compulsory study plan
2020/2021 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2019/2020 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
2019/2020 (B0714A150002) Control and Information Systems P English Ostrava 1 Compulsory study plan
2019/2020 (B0714A060011) Telecommunication Technology P English Ostrava 1 Compulsory study plan
2019/2020 (B0714A150004) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2019/2020 (B3973) Automotive Electronic Systems P English Ostrava 1 Compulsory study plan
2019/2020 (B0714A060009) Mobile Technology P English Ostrava 1 Compulsory study plan
2019/2020 (B0713A060006) Electrical Power Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (B0714A060017) Biomedical Technology P English Ostrava 1 Compulsory study plan
2019/2020 (B0714A060017) Biomedical Technology K English Ostrava 1 Compulsory study plan
2019/2020 (B0714A060013) Applied Electronics P English Ostrava 1 Compulsory study plan
2018/2019 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2018/2019 (B3973) Automotive Electronic Systems P English Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
2017/2018 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2017/2018 (B3973) Automotive Electronic Systems P English Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
2016/2017 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

### Assessment of instruction

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