Sobre o teorema de Kruskal de que todo tensor 3 × 3 × 3 tem posto no máximo 5

Abstract

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.