Abstract:
It is shown that the results of Strassen on existence of bilinear algorithm
with seven multiplications for multiplication of matrices of order 2 has the
following
simple interpretation: there exists a 7-dimensional algebra
with simple multiplication that is an extension of the algebra of matrices
of order 2. It is proved that exactly three such 7-dimensional algebras
exist. This work was supported by the Russian Foundation for Basic Research,
Grant 94-01-01206.
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