# 470-8724/01 – Linear Algebra (LA AVAT)

 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 Czech Year of introduction 2015/2016 Year of cancellation 2020/2021 Intended for the faculties USP Intended for study types Bachelor
Instruction secured by
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

### 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:

GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.

### Recommended literature:

GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149.

### Way of continuous check of knowledge in the course of semester

2 tests (15 pts.) Homework (15 pts.)

### Other requirements

There are no further requirements.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Systems of linear equations. 2. Gaussian elimination. 3. Matrix calculus, inverse matrices. 4. Vector spaces. 5. Base and solvability of systems of linear equations. 6. Linear maps. 7. Bilinear forms, determinants. 8. Quadratic forms. 9. Orthogonality, orthogonal projection, the method of least squares. 10. Eigenvalues and eigenvectors.

### Conditions for subject completion

Full-time form (validity from: 2015/2016 Summer semester, validity until: 2020/2021 Summer semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 30  10
Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (B3968) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner