# 470-2201/02 – Linear Algebra (LA1)

 Gurantor department Department of Applied Mathematics Credits 4 Subject guarantor doc. Ing. Dalibor Lukáš, Ph.D. Subject version guarantor doc. Mgr. Vít Vondrák, Ph.D. Study level undergraduate or graduate Study language Czech Year of introduction 2010/2011 Year of cancellation 2010/2011 Intended for the faculties FEI, USP Intended for study types Bachelor
Instruction secured by
GRU100 Ing. Ondřej Grunt, Ph.D.
HAS081 Ing. Martin Hasal
HEN50 RNDr. Ctibor Henzl, Ph.D.
HRT021 Ing. Rostislav Hrtus
JAH02 RNDr. Pavel Jahoda, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
POS220 Ing. Lukáš Pospíšil
STA545 Ing. Martin Stachoň
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

### 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

### 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

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

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