457-0918/01 – Matrix Analysis (MXA)

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 introduction1998/1999Year of cancellation2009/2010
Intended for the facultiesFEIIntended 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

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

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.

Compulsory literature:

S. Barnett: Marices, Methods and Applications, Clarendon Press, Oxford 1994. F. R. Gantmacher: The theory of matrices. Vol. 1-2. 1959 translation. (English) Providence, RI: AMS Chelsea Publishing, Providence 1959, 1998. Carl D. Mayer, Matrix Analysis and Applied Numerical Linear Algebra, SIAM Philadelphia 1997. H. Schnaider, G. P. Barker, Matrices and Linear Algebra, Dover, New York 1989.

Recommended literature:

J. W. Demmel, Applied Numerical Linear Algebra, SIAM Philadelphia 1997.

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 relations in description of electrical networks and mechanical systems. Vektor space, linear mapping, approximation of differential operators. Matrix of a linear mapping, similarity. Rank and defect, composition, principle of superposition. Bilineární and quadratic forms. Matrices and classification of bilinear and quadratic forms, application of LDLT decomposition. Scalar product and orthogonality. Norms, orthogonal systems of vectors, variational principle and the least square method. skládání lineárních zobrazení, linearita inverzního zobrazení a princip superpozice. Matice lineárního zobrazení, podobnost. Projectors. Rotace, reflections, QR decomposition and solution of systems of linear equations. Conjugate gradient method. Eigenvalues and eigenvectors.. Definition, basic properties, localization of eigenvalues. Spectral decomposition of a symmetric matrix. Matrix calculus fr symmetric matrices, polar decomposition, singular decomposition and gneralized inverse matrix. Jordan form and matrix functions, applications to ODE. Generalizations to infinite dimension. Banach space, Hilbert space.

Conditions for subject completion

Full-time 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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Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
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 Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
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 Choice-compulsory study plan
2008/2009 (P2646) Information Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-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
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics 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
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
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 Choice-compulsory study plan
2005/2006 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
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
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics 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
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics 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
2002/2003 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava 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
2001/2002 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan

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