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

abstract

• 2018 Elsevier B.V. This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank 23 decompositions for the 33 matrix multiplication tensor M 3 . All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and admits an unexpected symmetry group of order 12. We establish basic information regarding symmetry groups of decompositions and outline two approaches for finding new rank decompositions of M n for larger n.

authors

• Landsberg, Joseph

published proceedings

• JOURNAL OF PURE AND APPLIED ALGEBRA

author list (cited authors)

• Ballard, G., Ikenmeyer, C., Landsberg, J. M., & Ryder, N.

citation count

• 7

complete list of authors

• Ballard, Grey||Ikenmeyer, Christian||Landsberg, JM||Ryder, Nick

publication date

• August 2019

publisher

• Elsevier  Publisher

published in

• Journal of Pure and Applied Algebra  Journal

keywords

• Alternating Least Squares
• Matrix Multiplication Complexity

Digital Object Identifier (DOI)

• 10.1016/j.jpaa.2018.10.014

start page

• 3205

end page

• 3224

volume

• 223

issue

• 8

URL

• http://dx.doi.org/10.1016/j.jpaa.2018.10.014