230-0266/02 – Linear Algebra (LA)

Gurantor departmentDepartment of MathematicsCredits10
Subject guarantordoc. Ing. Martin Čermák, Ph.D.Subject version guarantordoc. Ing. Martin Čermák, Ph.D.
Study levelpostgraduateRequirementCompulsory
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2020/2021Year of cancellation
Intended for the facultiesFASTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
CER365 doc. Ing. Martin Čermák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Part-time Examination 28+0

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

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

Part-time form (validity from: 2020/2021 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (P0732D260005) Civil Engineering K English Ostrava Compulsory study plan
2021/2022 (P0732D260005) Civil Engineering P English Ostrava Compulsory study plan
2020/2021 (P0732D260005) Civil Engineering P English Ostrava Compulsory study plan
2020/2021 (P0732D260005) Civil Engineering K English Ostrava Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner