Paper detail

On Kruskal's theorem that every 3 x 3 x 3 array has rank at most 5

In the first part of this paper, we consider 3 x 3 x 3 arrays with complex entries, and provide a complete self-contained proof of Kruskal's theorem that the maximum rank is 5. In the second part, we provide a complete classification of the canonical forms of 3 x 3 x 3 arrays over F_2; in particular, we obtain explicit examples of such arrays with rank 6.