470-6501/02 – Applied Linear Algebra (ALA)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesHGF, FEI, USP, FSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
KOV16 doc. Mgr. Petr Kovář, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, 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

Students will learn about the role of fundamental concepts of linear algebra in analysis of engineering problems, with their properties, classification, with special matrices that appear in applications, with matrix decompositions, spectral characteristics of matrices and with matrix functions.

Teaching methods

Lectures
Project work

Summary

The students will learn abaut fundamental concepts of linear algebra in the conext of applications in computer science and engineering.

Compulsory literature:

G. Strang, Introduction to Linear Algebra, 4th Edition, Wellesley-Cambridge Press

Recommended literature:

J. W. Demmel, Applied Numerical Linear Algebra, SIAM Philadelphia 1997. F. R. Gantmacher: The theory of matrices. Vol. 1-2. 1959 translation. (English)

Way of continuous check of knowledge in the course of semester

Continuous monitoring of study activities and assigned tasks during regular consultations. If some publication activity will be a part of the student's tasks, the relevant article would be presented in the course.

E-learning

Other requirements

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Linear mappings in elektric networks and mechanical systems. Vector space, linear mapping and matrices. Rank, defect, and composition of linear mappings, principle of superposition. Matrices of linear mappings and similarity. Bilinear and quadratic forms. Matrices and classification of bilinearr and quadratic forms, congruent matrices and LDLT decomposition. Scalar product nad orthogonality. Norms, variational principle, the least square method and projectors. Conjugate gradient method. Matrix transformations and solution of linear systems. Eigenvalues and eigenvectors, localization of eigenvalues. Spectral decomposition of symmetric matrix. Matrix calculus, singular decomposition and pseudoinverse matrices. Jordan form. Matrix calculus, applications.. Generalizations to infinite dimension. Banach and Hilbert spaces.

Conditions for subject completion

Part-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)		Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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

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2017/2018 (P2346) Mechanical Engineering (2302V006) Energy Engineering K English Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K English Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K English Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2017/2018 (P2658) Computational Sciences (2612V078) Computational Sciences P English Ostrava Choice-compulsory study plan
2017/2018 (P2658) Computational Sciences (2612V078) Computational Sciences K English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V013) Robotics P English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2302V006) Energy Engineering P English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V013) Robotics K English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2302V006) Energy Engineering K English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K English Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2016/2017 (P2658) Computational Sciences (2612V078) Computational Sciences P English Ostrava Choice-compulsory study plan
2016/2017 (P2658) Computational Sciences (2612V078) Computational Sciences K English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2302V006) Energy Engineering P English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V013) Robotics P English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2302V006) Energy Engineering K English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V013) Robotics K English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K English Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2015/2016 (P2658) Computational Sciences (2612V078) Computational Sciences P English Ostrava Choice-compulsory study plan
2015/2016 (P2658) Computational Sciences (2612V078) Computational Sciences K English Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2022/2023 Winter
2017/2018 Winter