Resumo:
The main objective of this dissertation is the study of the article written by M. Bremner and Jiaxiong
Hu “On Kruskal’s theorem that every 3×3×3 array has rank at most 5”, where the objective is to show
that the rank of every tensor 3×3×3 is at most 5, a case previously studied by Kruskal. To achieve this,
we will start with basic definitions and concepts of linear and multilinear algebra, we will continue with
tensors and their rank, showing properties necessary for the development of the subject. We will come
to the specific study of the tensors 2×2×2 and an algorithm to find their rank, at the end we will study
the tensors 3×3×2 and 3×3×3 showing results and examples about them to reach the demonstration
of the main theorem with everything that is necessary to understand it.
