457-0901/01 – Applied Mathematics I (Matrix analysis). (VSMI)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1992/1993Year of cancellation2009/2010
Intended for the facultiesIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 2+0
Distance Credit and Examination 2+0

Subject aims expressed by acquired skills and competences

To present basic results and algorithms of matrix analysis with stress on applications in numerical analysis and technics.

Teaching methods

Summary

Basic step in the solution of many engineering problems is their reduction to the matrix problem. The students will have opportunity to understand the role of matrices in technical problems, to learn about basic properties of matrices, special matrices, matrix decompositions, spectral theory and matrix calculus.

Compulsory literature:

G. Strang, Linear Algebra and its Application, Academic Press, New York 1980. G. H. Golub, and C. van Loan, Matrix Computations, The John Hopkins University Press, London 1989. L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM Philadelphia 1997. ISBN 0-89871-361-7.

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: 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

Combined form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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2009/2010 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
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2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Compulsory study plan
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2008/2009 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
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2008/2009 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
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2008/2009 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
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2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics K Czech Ostrava Compulsory study plan
2008/2009 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
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2007/2008 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
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2007/2008 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
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2007/2008 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
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2006/2007 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
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2006/2007 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
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2006/2007 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2006/2007 (P3925) Management of Industrial Systems (3902V777) Řízení jakosti P Czech Ostrava Choice-compulsory study plan
2006/2007 (P3925) Management of Industrial Systems (3902V888) Řízení a ekonomika podniku P Czech Ostrava Choice-compulsory study plan
2006/2007 (P3925) Management of Industrial Systems (3902V999) Automatizace technologických procesů P Czech Ostrava Choice-compulsory study plan
2006/2007 (P3925) Management of Industrial Systems (3902V777) Řízení jakosti K Czech Ostrava Choice-compulsory study plan
2006/2007 (P3925) Management of Industrial Systems (3902V888) Řízení a ekonomika podniku K Czech Ostrava Choice-compulsory study plan
2006/2007 (P3925) Management of Industrial Systems (3902V999) Automatizace technologických procesů K Czech Ostrava Choice-compulsory study plan
2006/2007 (P3607) Civil Engineering (3607V025) Theory of Contruction P Czech Ostrava Optional study plan
2006/2007 (P3607) Civil Engineering (3607V025) Theory of Contruction K Czech Ostrava Optional study plan
2005/2006 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Compulsory study plan
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2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
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2001/2002 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
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Occurrence in special blocks

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