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Linear Algebra
| Type of study | Doctoral |
|---|---|
| Language of instruction | Czech |
| Code | 230-0266/01 |
| Abbreviation | LA |
| Course title | Linear Algebra |
| Credits | 10 |
| Coordinating department | Department of Mathematics |
| Course coordinator | doc. Ing. Martin Čermák, Ph.D. |
Subject syllabus
• Linearity in technology.
• Vector space, linear representation, matrix matrices.
• Rank and defect of linear representations, the composition of linear representations, the principle of superposition.
• Linear mapping matrix, similarity.
• Bilinear and quadratic forms.
• Matrix and classification of bilinear and quadratic forms, congruence, and LDLT decomposition.
• Scalar product and orthogonality.
• Standards, variational principle, least squares method, projectors.
• Combined gradient method.
• Rotation, mirroring, QR decomposition, and system solutions.
• Eigenvalues and vectors, localization of eigenvalues.
• Spectral decomposition of a symmetric matrix and its consequences.
• Symmetric matrix functions, polar decomposition, singular decomposition, and pseudoinverse.
• Jordan's form.
• Vector space, linear representation, matrix matrices.
• Rank and defect of linear representations, the composition of linear representations, the principle of superposition.
• Linear mapping matrix, similarity.
• Bilinear and quadratic forms.
• Matrix and classification of bilinear and quadratic forms, congruence, and LDLT decomposition.
• Scalar product and orthogonality.
• Standards, variational principle, least squares method, projectors.
• Combined gradient method.
• Rotation, mirroring, QR decomposition, and system solutions.
• Eigenvalues and vectors, localization of eigenvalues.
• Spectral decomposition of a symmetric matrix and its consequences.
• Symmetric matrix functions, polar decomposition, singular decomposition, and pseudoinverse.
• Jordan's form.
E-learning
Literature
Z. Dostál, V. Vondrák, D. Lukáš, Lineární algebra, VŠB-TU Ostrava 2012, http://mi21.vsb.cz/modul/linearni-algebra
Z. Dostál, Lineární algebra, VŠB-TU Ostrava 2000
Z. Dostál, L. Šindel, Lineární algebra pro kombinované a distanční studium, VŠB-TU Ostrava 2003
H. Anton, Elementary Linear Algebra, J. Wiley , New York 1991
Dianne P. O'Leary, Scientific Computing with Case Studies, SIAM, Philadelphia 2009
Z. Dostál, Lineární algebra, VŠB-TU Ostrava 2000
Z. Dostál, L. Šindel, Lineární algebra pro kombinované a distanční studium, VŠB-TU Ostrava 2003
H. Anton, Elementary Linear Algebra, J. Wiley , New York 1991
Dianne P. O'Leary, Scientific Computing with Case Studies, SIAM, Philadelphia 2009
Advised literature
L. Motl, M. Zahradník, Používáme lineární algebru. Karolinum, Praha 2003.
K. Výborný, M. Zahradník, Používáme lineární algebru. Karolinum, Praha 2004.
B. Budinský, J. Charvát, Matematika I, SNTL Praha 1987
S. Barnet, Matrices, Methods and Applications, Clarendon Press, Oxford 1994
H. Schnaider, G. P. Barker, Matrices and Linear Algebra, Dover, New York 1989
K. Výborný, M. Zahradník, Používáme lineární algebru. Karolinum, Praha 2004.
B. Budinský, J. Charvát, Matematika I, SNTL Praha 1987
S. Barnet, Matrices, Methods and Applications, Clarendon Press, Oxford 1994
H. Schnaider, G. P. Barker, Matrices and Linear Algebra, Dover, New York 1989