The concept of tensor products is ubiquitous in the scientific literature. In this talk, we restrict our attention to the tensor product of a finite number of finite-dimensional vector spaces. The bulk of the research on such tensor products assumes the underlying field to be the real numbers or the complex numbers. 

With the advancement of our knowledge and technology, the need for efficient algorithms to verify certain properties or compute numerical data from a given tensor has become a very popular research topic. In the first part of this talk, we will give a short introduction explaining the main concepts and research problems.

In the second part, we will focus on the case where the underlying field is finite.