1) basics: Notation - Vector, Matrix, Modeling linear Systems, state-space discription, Fourier, Laplace und Z-Transform, sampling theorems 2) Vector spaces and linear algebra: metric spaces, groups, topologic terms, supremum and infimum, series, Cauchy series, linear combinations, lineare independency, basis and dimension, norms and normed vector spaces, inner vector products and inner produkt spaces, Induced norms and Cauchy-Schwarz Inequality, Orthogonality, Hilbert and Banach spaces, 3) Representation and Approximation in Vector spaces: Approximation problem im Hilbert space, Orthogonality principle, Minimisation with gradient method, Least Square Filterung, linear regression, Signal transformation and generalized Fourier series, Examples for orthogonal Funktions, Wavelets 4) Linear Operators: Linear Functionals, norms on Operators, Orthogonal sub spaces, null space and Range, Projections, Adjoint Operators, Matrix rank, Inverse and condition number 5) Kronecker Products: Kronecker Products and Sums, DFT, FFT, Hadamard Transformations, Special Forms of FFT, Split Radix FFT, Overlab add and save Methods, examples to OFDM, Vec-Operator
mathematically oriented part of bacc studies is assumed to be passed! for example, Math I-III, Signals and Systems I and II, Electrodynamics
