The geometry of rank decompositions of matrix multiplication II: 3 x 3 matrices

Ballard, Grey, Ikenmeyer, Christian, Landsberg, JM and Ryder, Nick (2019) The geometry of rank decompositions of matrix multiplication II: 3 x 3 matrices. JOURNAL OF PURE AND APPLIED ALGEBRA, 223 (8). pp. 3205-3224.

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Official URL: http://dx.doi.org/10.1016/j.jpaa.2018.10.014

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.

Item Type:	Article
Additional Information:	9 pages
Uncontrolled Keywords:	Matrix multiplication complexity, Alternating least squares
Depositing User:	Symplectic Admin
Date Deposited:	06 Feb 2020 08:42
Last Modified:	19 Jan 2023 00:04
DOI:	10.1016/j.jpaa.2018.10.014
Open Access URL:	https://arxiv.org/pdf/1801.00843
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3073622