# 470-2201/01 – 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 summer Study language Czech Year of introduction 2010/2011 Year of cancellation Intended for the faculties USP, FS, FEI Intended for study types Bachelor
Instruction secured by
NAG0013 Ing. Judita Buchlovská Nagyová
SAR0066 Mgr. Martina Ćosićová
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.
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. Conditions for credit: Minimum 10 points 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: Complex numbers Solution of systems of linear equations by elimation based methods Algebra of arithmetic vectors and matrices Inverse matrix Vector space Spaces of functions Derivation and integration of piece-wise linear functions Linear mapping Bilinear and quadratic forms Determinants Eigenvalues and eigenvectors An introduction to analytic geometry 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

Part-time form (validity from: 2012/2013 Winter semester, validity until: 2020/2021 Summer semester)
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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### Occurrence in special blocks

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