  Multilinear and tensor decompositions are a popular tool in linear and
multilinear algebra and have a wide range of important applications to modern
computing. Our paper of 1972 presented the first nontrivial application of such
decompositions to fundamental matrix computations and was also a landmark in
the history of the acceleration of matrix multiplication. Published in 1972 in
Russian, it has never been translated into English. It has been very rarely
cited in the Western literature on matrix multiplication and never in the works
on multilinear and tensor decompositions. This motivates us to present its
translation into English, together with our brief comments on its impact on the
two fields.
