ИСТИНА

We consider the problem of finding a general case proof of the generic rank conjecture for complex tensors of third order. With minor exceptions the conjecture prescripts the generic rank of each tensor space to have the value computing as an expression depending only on sizes of tensor space. That statement has been proven in some particular cases by various authors. We propose an outline of a proof for the generic rank's expression for a class of tensor spaces known as ones with a perfect shape. In our reasoning the splitting technique is used for rank evaluation of Jacobian-like matrices originally suggested for special cases of the conjecture by V. Strassen in 1983. We also analyze the possibilities of using the specified technique as an approach of proving the conjecture in the general case.