470-2202/02 – Linear Algebra (LA-IT)

Gurantor department	Department of Applied Mathematics	Credits	8
Subject guarantor	doc. Ing. Petr Beremlijski, 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
Login	Name	Tuitor	Teacher giving lectures
BER95	doc. Ing. Petr Beremlijski, Ph.D.
KUR138	Ing. Pavlína Forstová Kuráňová, Ph.D.
HAP014	Ing. Václav Hapla, Ph.D.
HOR33	doc. Ing. David Horák, Ph.D.
HRT021	Ing. Rostislav Hrtus, Ph.D.
JAH02	RNDr. Pavel Jahoda, Ph.D.
KOT237	Ing. Petr Kotas
LUK76	doc. Ing. Dalibor Lukáš, Ph.D.
JAN939	Ing. Kateřina Martinovičová, Ph.D.
MEN060	Ing. Martin Menšík
RAD0031	Mgr. Kristina Motyčková, Ph.D.
SIM46	Mgr. Lenka Přibylová, Ph.D.
RAP027	Ing. Lukáš Rapant, Ph.D.
RON012	Ing. Aleš Ronovský
SIN29	RNDr. Libor Šindel
STA545	Ing. Martin Stachoň
VLA04	Ing. Oldřich Vlach, Ph.D.
S1A64	RNDr. Petra Vondráková, Ph.D.
ZDR060	Ing. Adam Zdráhala

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	2+4
Part-time	Credit and Examination	12+12

Subject aims expressed by acquired skills and competences

To supply working knowledge of basic concepts of linear algebra including their geometric and computational meaning, in order to enable to use these concepts in solution of basic problems of linear algebra. Student should also learn how to use the basic tools of linear algebra in applications.

Teaching methods

Lectures
Tutorials
Project work

Summary

Linear algebra is one of the basic tools of formulation and solution of engineering problems. The students will get in an elementary way basic concepts and comutational skills of linear algebra, including algorithmic aspects that are important in computer implementation.

Compulsory literature:

H. Anton, Elementary Linear Algebra, J. Wiley , New York 1991.

Recommended literature:

S. Barnet, Matrices, Methods and Applications, Clarendon Press, Oxford 1994 H. Schnaider, G. P. Barker, Matrices and Linear Algebra, Dover, New York 1989

Way of continuous check of knowledge in the course of semester

Verification of study: Test on solution of linear systems and matrix algebra (max 5m) Test on vector spaces, linear mapping and multilinear algebra (max 5m) Homeworks (12m) 4 sets of 3 examples each for 1m. Semestral project (8m) 2 examples each for 4m. Complex numbers and spectral theory. Conditions for credit: Minimum 10 marks on tests, the homeworks. and semestral project.

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: An introduction to matrix calculus Solution of systems of linear equations Inverse matrices LU factorization Vector spaces and subspaces Basis and dimension of vector spaces Linear mapping Derivation and definite integral of piecewise linear functions Bilinear and quadratic forms Determinants Eigenvalues and eigenvectors An introduction to analytic geometry Exercises: Computing with complex numbers Practicing algebra of arithmetic vectors and matrices Solution of systems of linear equations Evaluation of inverse matrix LU factorization and solution of systems of linear eq. 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 Matrices 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

Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Zaměření	Form	Study language	Tut. centre	Year	W	S	Type of duty

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

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