1) Basics: Notation - Vector, Matrix, Modeling linear Systems, state-space description, Fourier, Laplace, and Z-Transform, sampling theorems
2) Vector spaces and linear algebra: metric spaces, groups, topologic terms, supremum and infimum, series, Cauchy series, linear combinations, linear independence, basis and dimension, norms and normed vector spaces, inner vector products and inner product spaces, Induced norms and Cauchy-Schwarz Inequality, Orthogonality, Hilbert and Banach spaces,
3) Representation and Approximation in Vector spaces: Approximation problem in Hilbert space, Orthogonality principle, Minimisation with gradient method, Least Square Filtering, linear regression, machine learning, Signal transformation and generalized Fourier series, Examples for orthogonal Functions, Wavelet
4) Linear Operators: Linear Functionals, norms on Operators, Orthogonal subspaces, 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, Overlap add and save Methods, circulant matrices, examples to OFDM, Vec-Operator, Big Data, asymptotic equivalence of Toeplitz and circulant matrices
