# 470-2201/03 – Linear Algebra (LA1)

 Gurantor department Department of Applied Mathematics Credits 4 Subject guarantor doc. Ing. Dalibor Lukáš, Ph.D. Subject version guarantor doc. Ing. Dalibor Lukáš, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language English Year of introduction 2015/2016 Year of cancellation Intended for the faculties USP, FEI, FS Intended for study types Bachelor
Instruction secured by
KOV74 Mgr. Tereza Kovářová, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, 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: 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.

### 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: 2022/2023 Winter semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 30 (30) 10
Semester point score Other task type 30  10
Examination Examination 70  21 3
Mandatory attendence participation: Attendance at discussions is obligatory (70 %). Attendance at lectures is expected.

Show history

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

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
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 (B0714A150004) Computer Systems for the Industry of the 21st. Century 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

Předmět neobsahuje žádné hodnocení.