470-2202/03 – Linear Algebra (LA-IT)

Gurantor departmentDepartment of Applied MathematicsCredits8
Subject guarantordoc. Ing. Petr Beremlijski, Ph.D.Subject version guarantordoc. Ing. Petr Beremlijski, Ph.D.
Study levelundergraduate or graduate
Study languageEnglish
Year of introduction2015/2016Year of cancellation2015/2016
Intended for the facultiesFEI, USPIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BER95 doc. Ing. Petr Beremlijski, Ph.D.
COS004 Ing. Rajko Ćosić
KUR138 Ing. Pavlína Forstová Kuráňová, Ph.D.
HAP014 Ing. Václav Hapla, Ph.D.
HAS081 Ing. Martin Hasal, Ph.D.
JAH02 RNDr. Pavel Jahoda, Ph.D.
JAR091 Ing. Milan Jaroš, Ph.D.
JIR0013 Ing. Pavla Jirůtková
KRB0006 Ing. Matěj Krbeček
KUB59 RNDr. Michael Kubesa, Ph.D.
LIT40 Ing. Martina Litschmannová, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
MAL539 Ing. Lukáš Malý
JAN939 Ing. Kateřina Martinovičová, Ph.D.
RAP027 Ing. Lukáš Rapant, Ph.D.
RON012 Ing. Aleš Ronovský
SIN29 RNDr. Libor Šindel
THE021 Ing. Matyáš Theuer
MIK0063 Ing. Žaneta Vaníčková
S1A64 RNDr. Petra Vondráková, Ph.D.
ZAP150 Ing. Jan Zapletal, Ph.D.
Extent of instruction for forms of study
Form of studyWay 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 12m) Test on vector spaces, linear mapping and multilinear algebra (max 12m) Semestral project (max 6m) 2 examples each for 3m. Complex numbers and orthonormalization process. Conditions for credit: Minimum 10 marks on tests and semestral project.

E-learning

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: 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 Using supercomputer Anselm and linear algebra to solve engineering problems 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

Conditions for subject completion

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

Occurrence in study plans

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Occurrence in special blocks

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Assessment of instruction

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