470-4201/02 – Applied algebra (AA)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduateRequirementOptional
Year1Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
VLA04 Ing. Oldřich Vlach, 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 10+10

Subject aims expressed by acquired skills and competences

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

Teaching methods

Lectures
Tutorials

Summary

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.

Compulsory literature:

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

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

Two tests during the term.

E-learning

Další požadavky na studenta

There are no additional requirements imposed on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

• 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

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. 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
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType 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

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner