230-0266/02 – Linear Algebra (LA)
| Gurantor department | Department of Mathematics | Credits | 10 |
| Subject guarantor | doc. Ing. Martin Čermák, Ph.D. | Subject version guarantor | doc. Ing. Martin Čermák, Ph.D. |
| Study level | postgraduate | Requirement | Compulsory |
| Year | | Semester | winter + summer |
| | Study language | English |
| Year of introduction | 2020/2021 | Year of cancellation | |
| Intended for the faculties | FAST | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
The aim of the course is to acquaint students with the definitions of basic concepts of linear algebra. After completing this course, students will understand their geometric and computational significance and will be able to use their knowledge to solve the fundamental problems of linear algebra. Students will also be acquainted with selected application tasks that use concepts of linear algebra within the course.
Teaching methods
Lectures
Individual consultations
Summary
Compulsory literature:
Z. Dostál, V. Vondrák, D. Lukáš, Lineární algebra, VŠB-TU Ostrava 2012, http://mi21.vsb.cz/modul/linearni-algebra
Z. Dostál, Lineární algebra, VŠB-TU Ostrava 2000
Z. Dostál, L. Šindel, Lineární algebra pro kombinované a distanční studium, VŠB-TU Ostrava 2003
H. Anton, Elementary Linear Algebra, J. Wiley , New York 1991
Dianne P. O'Leary, Scientific Computing with Case Studies, SIAM, Philadelphia 2009
Recommended literature:
L. Motl, M. Zahradník, Používáme lineární algebru. Karolinum, Praha 2003.
K. Výborný, M. Zahradník, Používáme lineární algebru. Karolinum, Praha 2004.
B. Budinský, J. Charvát, Matematika I, SNTL Praha 1987
S. Barnet, Matrices, Methods and Applications, Clarendon Press, Oxford 1994
H. Schnaider, G. P. Barker, Matrices and Linear Algebra, Dover, New York 1989
Additional study materials
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Tests, semester project, consultations for the subject of dissertation thesis and the publications of the student, oral exams.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
• Linearity in technology.
• Vector space, linear representation, matrix matrices.
• Rank and defect of linear representations, the composition of linear representations, the principle of superposition.
• Linear mapping matrix, similarity.
• Bilinear and quadratic forms.
• Matrix and classification of bilinear and quadratic forms, congruence, and LDLT decomposition.
• Scalar product and orthogonality.
• Standards, variational principle, least squares method, projectors.
• Combined gradient method.
• Rotation, mirroring, QR decomposition, and system solutions.
• Eigenvalues and vectors, localization of eigenvalues.
• Spectral decomposition of a symmetric matrix and its consequences.
• Symmetric matrix functions, polar decomposition, singular decomposition, and pseudoinverse.
• Jordan's form.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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