457-0523/01 – Linear Algebra (LA1R)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction1999/2000Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
HOR33 doc. Ing. David Horák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 4+2
Combined Credit and Examination 4+2

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, to understand their relation and some applications in modern engineering.

Teaching methods

Summary

Linear algebra is a basic tool for formulation and solution of engineering problems. The students will first learn about finite methods of solution of linear system and about matrix calculus. Then they will study general concepts like vector spaces, linear mapping, bilinear and quadratic form, eigenvalue and eigenvector. The course comprises also introduction to analytic geometry. This particular cours stresses understanding and mutual relations of basic concepts as they are used in both modern engineering and informatics. It is designed for students who consider higher degrees (including M.Sc.), especially in those parts of applications that require deeper theoreticat background

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, matrix algebra and vector spaces (max 8m) Test on linear mapping, multilinear algebra and eigencetors (max 7m) Home assignment (15m) Conditions for credit: Minimum 15 marks on tests and the home assignments

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Complex numers Solution of systems of linear equations by elimination Algebra aof arithmetic vectors and matrices Inverse matrices Vekctor space Vector spaces of functions Derivation and definite integral of piecewise 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 Matrices of bilinear and quadratic forms Evaluation of determinants Evaluation of eigenvalues and eigenvectors Computational examples from analytic geometry Computer labs: Linear algebra in MATLAB.

Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 1 Compulsory study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2646) Information Technology (2612R025) Computer Science and Technology P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2646) Information Technology (2612R025) Computer Science and Technology K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner