Abstract
In 1973 Strassen conjectured that additivity holds for bilinear maps, namely that the computational complexity of simultaneously executing two bilinear maps is the same as the sum of the complexities of the individual bilinear maps. In complexity theory, of particular interest is the matrix multiplication.
I will rephrase Strassen's conjecture in terms of tensor rank and show that it holds for three-factor tensors, whenever the dimension of one of the involved vector spaces is at most two.
This is joint work in progress with J. Buczynski.