Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | prof. RNDr. Zdeněk Dostál, DSc. | Subject version guarantor | prof. RNDr. Zdeněk Dostál, DSc. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2003/2004 | Year of cancellation | 2009/2010 |

Intended for the faculties | FEI | Intended for study types | Bachelor |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

DOS35 | prof. RNDr. Zdeněk Dostál, DSc. | ||

VON15 | doc. Mgr. Vít Vondrák, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 2+2 |

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.

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.

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.

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.

Subject has no prerequisities.

Subject has no co-requisities.

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).

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (145) | 51 | 3 |

Examination | Examination | 100 | 0 | 3 |

Exercises evaluation | Credit | 45 | 0 | 3 |

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Conditions for subject completion and attendance at the exercises within ISP:

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

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