Emil Ringh: What is rank? - An introduction to tensors and low-rank tensor techniques

What is a tensor, and how do we define its rank? In this talk I will introduce the basic concepts of tensors and tensor rank, as it is presented in the literature.
Different decompositions comes with different notions of rank, and I will briefly cover the most common ones:  Canonical rank and the CP decomposition, Tucker rank and the Tucker decomposition, as well as TT-rank and Tensor Train decomposition. Focus will be on theoretical aspects of tensors and tensor decompositions, but aimed towards numerical treatment.