Linear Algebra

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Course Unit Code Number of ECTS Credits Allocated Type of Course Unit * Level of Course Unit * Year of Study * 470-2201/01 4 ECTS credits Compulsory First Cycle First Year Summer Semester Face-to-face Czech, English Course succeeds to compulsory courses of previous semester LUK76 doc. Ing. Dalibor Lukáš, Ph.D. JAH02 RNDr. Pavel Jahoda, Ph.D. Linear algebra is a basic tool of formulation and effective solution of technical problems. The students will get knowledge of basic concepts and computational skills of linear algebra. Many engineering problems lead to solution of large-scale systems of linear equations. The aim of this course is to introduce fundamental notions of linear algebra and relate them to applications in electrical engineering. First we shall learn how to solve real and complex systems of linear equations by Gauss elimination method. The systems arises in the analysis of electrical circuits. In an intuitive manner we shall introduce notions such as base of a vector space, linear transformation and using them we will formulate basic linear problems. In the second part of the course, we shall focus on quadratic forms, which are closely related e.g. to electrical potential energy. Further we shall study orthogonality of functions, on which e.g. Fourier analysis of signals rely. Finally, we shall introduce spectral theory with applications to analysis of resonances. Lectures: Complex numbers Solution of systems of linear equations by elimation based methods Algebra of arithmetic vectors and matrices Inverse matrix Vector space Spaces of functions Derivation and integration of piece-wise linear functions Linear mapping Bilinear and quadratic forms Determinants Eigenvalues and eigenvectors An introduction to analytic geometry Exercises: Arihmetics of complex numbers Solution of systems of linear equations Practicing algebra of arithmetic vectors and matrices Evaluation of inverse matrix Examples of vector spaces and deduction from axioms Evaluation of coordinates of a vector in a given basis Examples of functional spaces Examples of linear mappings and evaluation of their matrices Mtrices of bilinear and quadratic forms Evaluation of determinants Evaluation of eigenvalues and eigenvectors Computational examples from analytic geometry G. Strang, Video lectures of Linear Algebra on MIT. R.A. Horn, C.R. Johnson, Matrix Analysis. Cambridge University Press 1990. Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM 2003. Z. Dostál, Lineární algebra, VŠB-TU Ostrava 2000. G. Strang, Video lectures of Linear Algebra on MIT. G.H. Golub, C.F. Van Loan, Matrix Computations. The Johns Hopkins University Press 2013. L.N. Trefethen, D. Bau. Numerical Linear Algebra. SIAM 1997. J. Liesen, Z. Strakoš, Krylov Subspace Methods: Principles and Analysis. Oxford University Press 2012. Z. Dostál, L. Šindel, Lineární algebra pro kombinované a distanční studium, VŠB-TU Ostrava 2003 G.H. Golub, C.F. Van Loan, Matrix Computations. The Johns Hopkins University Press 2013 Lectures, Tutorials Exercises evaluation and Examination Credit and Examination 100 (100) 51 Exercises evaluation Credit 30 (30) 10 Homework 1 Project 7 0 Test 1 Written test 8 0 Homework 2 Project 8 0 Test 2 Written test 7 0 Examination Examination 70 21