470-8544/01 – Matrix Analysis (MA)
Gurantor department | Department of Applied Mathematics | Credits | 5 |
Subject guarantor | prof. RNDr. Zdeněk Dostál, DSc. | Subject version guarantor | prof. RNDr. Zdeněk Dostál, DSc. |
Study level | undergraduate or graduate | Requirement | Choice-compulsory |
Year | 2 | Semester | winter |
| | Study language | Czech |
Year of introduction | 2010/2011 | Year of cancellation | 2013/2014 |
Intended for the faculties | HGF | Intended for study types | Follow-up Master |
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
Other requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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