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.
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.
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.