457-0517/01 – Linear Algebra II (LA2)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
VON15 doc. Mgr. Vít Vondrák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

To expand the knowledge of the students by concepts that are important in understanding of modern methods used in informatics and numerical solution of engineering problems.

Teaching methods

Summary

Advanced concepts of linear algenra are key ingredients in solving of many engineering problems such as signal analysis, implemetation of search engins, optimal control or numerical solution of differential equations. In this course, the students can expand their knowledge of linear algebra by working knowledge of concepts that are important in understanding of modern methods used in informatics and numerical solution of engineering problems with a special stress on matrix decompositions and the spectral theory.

Compulsory literature:

G. Strang, Linear Algebra and its Application, Academic Press, New York 1980. G. H. Golub, and C. van Loan, Matrix Computations, The John Hopkins University Press, London 1989. L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM Philadelphia 1997. ISBN 0-89871-361-7.

Recommended literature:

Way of continuous check of knowledge in the course of semester

Verification of study: Written test on linear mapping and bilinear forms (maximum 10 marks). Written test on spectral theoryi (maximum 10 marks). Conditions for credit: Completed project and minimum 15 marks on the tests and projects.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Matrix transformations (Gauss, Jacobi and Hausholder) and decompositions. Algebraick operations and structures. Matrix of linear mapping, change of basis, similarity of matrices. Matrix of bilinear form, change of basis, congruency of syymetric and diagonal matrices. Variational methods for matrices, least squares and projectors. Localization of eigenvalues.l Spectral decomposition of a symmetric matrix. Scalar function of a symmetric matrix. Polar decomposition. Singular decomposition, condition number. Pseudoinverse matrices. Jordan form. Exercises: Evaluation of LU and QU decomposition. Examples of algebraic structures.. Evaluation of the matrix of a linear mapping. Evaluation of matrix of a bilinear form. Classification of bilinear and quadratic forms. Numerical solution of the least square problems. Ecaluation of the spectral decomposition. Evalution of matrix functions. Localization of eigenvalues based on cogruency and similarity. Solution of singular systems and applications of pseudoinverse matrices. Selected applications of linear algebra (coding, signal analysis, design of search engins, design of efficient numerical algorithms, ... Projects: Aplication oriented project in MATLAB (maximum 10 marks).

Conditions for subject completion

Full-time 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
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 2 Compulsory study plan
2009/2010 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 2 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 2 Compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner