The matrix capacity of a tensor

In 1990, D. Coppersmith and S. Winograd published an estimate of the amount of arithmetic operations necessary for the multiplication of square matrices n?×?n, which equals O(n ^2.3755). In this article, we make a systematization of the theoretical instruments that were used by D. Coppersmith and S. Winograd for their estimate. The improved estimate O(n ^2.373) is one of the results of this systematization.