The Geometry of Rank Decompositions of Matrix Multiplication I: 2 x 2 Matrices Academic Article

abstract

• 2017, 2017 Taylor & Francis Group, LLC. 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 establishing the symmetry group of Strassen's algorithm, and present two particularly nice subfamilies in the Strassen family of decompositions.

authors

• Landsberg, Joseph

published proceedings

• EXPERIMENTAL MATHEMATICS

author list (cited authors)

• Chiantini, L., Ikenmeyer, C., Landsberg, J. M., & Ottaviani, G.

citation count

• 12

complete list of authors

• Chiantini, Luca||Ikenmeyer, Christian||Landsberg, JM||Ottaviani, Giorgio

publication date

• July 2019

publisher

• Taylor & Francis  Publisher

published in

• Experimental Mathematics  Journal

keywords

• Matrix Multiplication
• Symmetries
• Tensor Decomposition
• Tensor Rank

Digital Object Identifier (DOI)

• 10.1080/10586458.2017.1403981

start page

• 322

end page

• 327

volume

• 28

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1080%2F10586458.2017.1403981