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, Wavelet
4) Linear Operators: Linear Functionals, norms on Operators, Orthogonal sub spaces, null space and Range, Projections, Adjoint Operators, Matrix rank, Inverse and condition number, matrix decompositions, subspace methods: pisarenko, music, esprit, singular value decomposition.
5) Kronecker Products: Kronecker Products and Sums, DFT, FFT, Hadamard Transformations, Special Forms of FFT, Split Radix FFT, Overlab add and save Methods, circulant matrices, examples to OFDM, Vec-Operator, Big Data, asymptotic equivalence of Toeplitz and circulant matrices.
Textbook: Moon, Stirling, Mathematical Methods and Algorithms
An addional script together with a copy of the presented slides is available in the graphical center
