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Paper

#### The Geometry of Rank Decompositions of Matrix Multiplication I: 2x2 Matrices

##### Fulltext (public)

arXiv:1610.08364.pdf

(Preprint), 162KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Chiantini, L., Ikenmeyer, C., Landsberg, J. M., & Ottaviani, G. (2016). The Geometry of Rank Decompositions of Matrix Multiplication I: 2x2 Matrices. Retrieved from http://arxiv.org/abs/1610.08364.

Cite as: http://hdl.handle.net/11858/00-001M-0000-002C-4F8B-3

##### 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.