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Linear Algebra and Learning from Data

The course can be considered as a complement of the linear algebra courses you have studied at our department, but at a more advanced level.

We'll pay more attention on how to abstract relevant mathematics and structures from applications for example data and how to apply the theory you've studied. The course will start with some elementary elements in linear algebra e.g. SVD, principal components, matrix norms, generalized eigenvalues and interlacing eigenvalues. In particular we'll deal with these topics in a numerical sounding way. Later we'll turn to an interactive treatment of linear algebra and subjects from data.

Course contents

  • Basic computationally efficient algorithms for large matrices
  • Principal Component Analysis
  • Sparse and underdetermined systems and their relation to data compression
  • Construction of neural networks and models for deep learning
  • Fitting hyperparameters
  • Selected topics on particular types of matrices