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Lecturer(s)
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Koudela Libor, Mgr. Ph.D.
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Course content
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Matrices. Basic operations with matrices. Commuting matrices. Classification of matrices. Matrix trace. Linear space. Linear dependence and independence. Subspace and span. Generator, basis and dimension. Coordinates. Linear mappings and matrices. Superposition of mappings. Inverse mapping and inverse matrix. Regular and singular matrices. Transition matrix. Rank of a matrix. Elementary operations and multiplication of matrices. Matrix equivalence and similarity. Inner-product space. Orthogonal and orthonormal basis. Orthogonalization. Orthogonal matrices. Eigenvectors and eigenvalues. Diagonalization. Factorization. Jordan's canonical form. Matrices and quadratic forms.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Methods of individual activities, Skills training
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Learning outcomes
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Students will be able to apply obtained skills in solving concrete mathematical, technical and economic problems.
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Prerequisites
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Supposes examination from subject PMAT1.
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Assessment methods and criteria
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Written examination, Home assignment evaluation, Didactic test
Assignment - active attendance at seminars and succesfully answered final written test.
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Recommended literature
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ABADIR, K. M., MAGNUS, J. R. Matrix algebra. Cambridge, 2005.
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FREIDBERG, S.H. Linear algebra. Prentice Hall, 2003.
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KRAJNÍK, E. Maticový počet. Praha, Vydavatelství ČVUT, 2000.
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RAO, C.R., RAO, M.B. Matrix algebra and its Applications to Statistics and Econometrics. . Singapore, World Sciencific, 2004.
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SLOVÁK, J. Lineární algebra. Učební texty.. Brno, Masarykova univerzita, 1998.
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