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The geometry of rank decompositions of matrix multiplication I: 2x2 matrices (1610.08364v1)
Published 25 Oct 2016 in cs.CC and math.AG
Abstract: This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix multiplication decompositions, give a geometric proof of the theorem of Burichenko's theorem establishing the symmetry group of Strassen's algorithm, and present two particularly nice subfamilies in the Strassen family of decompositions.