@online{CILO:16,
TITLE = {The Geometry of Rank Decompositions of Matrix Multiplication I: 2x2 Matrices},
AUTHOR = {Chiantini, Luca and Ikenmeyer, Christian and Landsberg, J. M. and Ottaviani, Giorgio},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1610.08364},
EPRINT = {1610.08364},
EPRINTTYPE = {arXiv},
YEAR = {2016},
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.},
}