Gurantor department | Department of Applied Mathematics | Credits | 4 |

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

Study level | undergraduate or graduate | Requirement | Optional |

Year | 1 | Semester | summer |

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

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

Login | Name | Tuitor | Teacher giving lectures |

VLA04 | Ing. Oldřich Vlach, Ph.D. |

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

Form of study | Way of compl. | Extent |

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

Combined | Credit and Examination | 10+10 |

A sudent will get basic knowledge of linear and multilinear algebra and their applications in modern information technology.

Lectures

Tutorials

Vector space, orthogonality, special bases (hierarchical, Fourier, wavelets), linear mapping, bilinear an quadratic forms, matrix decompositions (spectral, Schur, SVD), Markov's precesses, Page Rank vector, linear algebra of huge matrices, low rank approximation of large matrices, quadratic programming, SVM, tensors. Applications in information technology.

N. Halko, P. G. Martinsson, J. A. Tropp: Finding Structure with Randomness:
Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,
SIAM REVIEW, Vol. 53, No. 2, (2011)217–288
Matrix Analysis for Scientists and Engineers
by Alan J. Laub, SIAM, Philadelphia
Alan J. Laub, Matrix Analysis for Scientists and Engineers, SIAM, Philadelphia, 2005

Tamara G. Kolda, Brett W. Bader. Tensor Decompositions and Applications, SIAM Review, Vol. 51, No. 3, (2009)455–500
Carl D. Meyer, Matrix analysis and applied linear algebra, SIAM, Philadelphia, 2000
Dianne P. O'Leary, Scientific Computing with Case Studies, SIAM, Philadelphia 2009

Two tests during the term.

There are no additional requirements imposed on the student.

Subject has no prerequisities.

Subject has no co-requisities.

• An introduction to matrix decompositions with motivation and applications
• Spectral decomposition of a symmetric matrix
• Applications of the spectral decomposition: matrix functions, convergence of iterative methods, extremal properties of the eigenvalues
• QR decomposition – rank of the matrix, atable solution of linear systems, reflection
• SVD – low rank approximations of a matrix, image deblurring, image compression
• Approximate decompositions of large matrices and related linear algebra
• Tensor approximations – Kronecker product, tensors, tensor SVD, tensor train, image debluring
• Variational principle and least squares
• Total least squares
• Minimization of a quadratic function with equality constraints – KKT, duality, basic algorithms, SVM,
• Analytic geometry with matrix decompositions
• Inverse problems – Tichonov regularization, applications

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

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 30 | 15 |

Examination | Examination | 70 | 21 |

Show history

Academic year | Programme | Field of study | Spec. | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 1 | Optional | study plan | |||

2019/2020 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 1 | Optional | study plan | |||

2018/2019 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 1 | Optional | study plan | |||

2018/2019 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 1 | Optional | study plan | |||

2017/2018 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 1 | Optional | study plan | |||

2017/2018 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 1 | Optional | study plan | |||

2016/2017 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 1 | Optional | study plan | |||

2016/2017 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 1 | Optional | study plan | |||

2015/2016 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 1 | Optional | study plan | |||

2015/2016 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 1 | Optional | study plan |

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