## 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 * 470-8724/01 4 ECTS credits Compulsory First Cycle First Year Summer Semester Face-to-face Czech Course succeeds to compulsory courses of previous semester LUK76 doc. Ing. Dalibor Lukáš, 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. 1. Systems of linear equations. 2. Gaussian elimination. 3. Matrix calculus, inverse matrices. 4. Vector spaces. 5. Base and solvability of systems of linear equations. 6. Linear maps. 7. Bilinear forms, determinants. 8. Quadratic forms. 9. Orthogonality, orthogonal projection, the method of least squares. 10. Eigenvalues and eigenvectors. GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149. DOSTÁL, Z., VONDRÁK, V.: Lineární algebra. Elektronická skripta VŠB-TU Ostrava, http://mi21.vsb.cz GOLUB, G.H., Van LOAN, C.H.: Matrix Computations. The Johns Hopkins University Press, 1996. ISBN-13: 978-0801854149. ŠINDEL, L.: Lineární algebra v příkladech. Skripta VŠB-TU Ostrava, 1999. Lectures, Tutorials Credit and Examination Credit and Examination 100 (100) 51 Credit Credit 30 10 Examination Examination 70 21