470-8544/01 – Matrix Analysis (MA)

Gurantor departmentDepartment of Applied MathematicsCredits5
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation2013/2014
Intended for the facultiesHGFIntended for study typesFollow-up Master
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+2

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

Lectures
Tutorials

Summary

Compulsory literature:

J. Laub, Matrix Analysis for Scientists and Engineers, SIAM, Philadelphia 2005

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

No additional requirements are imposed on the 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

Full-time form (validity from: 2010/2011 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30  15
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2012/2013 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Choice-compulsory study plan
2011/2012 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Choice-compulsory study plan
2010/2011 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner