1) Basics: Notation - Vector, Matrix, Modeling linear Systems, state-space discription, 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 independency, 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 im 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 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
The lecture is supposed to be held in a hybrid mode, thus with partial presence if this is possible.
first class: Fr., 1.10.2021, 8:30 - 10:00,in presence!
We offer on Fridays exercises in presence mode as well as two dates for questions and discussions (also Fridays).
All lectures will be provided with audiotaping and the students may use the offered material for self-studies.
