4 research outputs found
Laderman matrix multiplication algorithm can be constructed using Strassen algorithm and related tensor's isotropies
In 1969, V. Strassen improves the classical~2x2 matrix multiplication
algorithm. The current upper bound for 3x3 matrix multiplication was reached by
J.B. Laderman in 1976. This note presents a geometric relationship between
Strassen and Laderman algorithms. By doing so, we retrieve a geometric
formulation of results very similar to those presented by O. Sykora in 1977
Non-existence of a short algorithm for multiplication of matrices with group
One of prospective ways to find new fast algorithms of matrix multiplication
is to study algorithms admitting nontrivial symmetries. In the work possible
algorithms for multiplication of matrices, admitting a certain group
isomorphic to , are investigated. It is shown that there
exist no such algorithms of length . In the first part of the work,
which is the content of the present article, we describe all orbits of length
of on the set of decomposable tensors in the space , where is the space of complex
matrices. In the second part of the work this description will be used to prove
that a short algorithm with the above-mentioned group does not exist.Comment: 19 pp. Accepted for publication in Proceedings of the Institute of
mathematics (of Academy of Sciences of Belarus