470-6501/01 – 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
Web linkStudy languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFS, HGF, USP, FEIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
BLA19 prof. RNDr. Radim Blaheta, CSc.
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
SNA57 prof. RNDr. Václav Snášel, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Combined Examination 28+0

Subject aims expressed by acquired skills and competences

Students will learn about the role of matrices 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

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

E-learning

Další požadavky na studenta

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

Prezenční form (validity from: 2013/2014 zimní semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Zkouška Zkouška  

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
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2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
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2010/2011 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1701) Physics K Czech Ostrava Optional study plan
2010/2011 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Optional study plan
2010/2011 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner