English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Paper

The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices

MPS-Authors
/persons/resource/persons202366

Ikenmeyer,  Christian
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

External Ressource
No external resources are shared
Fulltext (public)

arXiv:1801.00843.pdf
(Preprint), 319KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Ballard, G., Ikenmeyer, C., Landsberg, J. M., & Ryder, N. (2018). The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices. Retrieved from http://arxiv.org/abs/1801.00843.


Cite as: http://hdl.handle.net/21.11116/0000-0001-3F64-9
Abstract
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 $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. 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 $M_{\langle n\rangle}$ for larger $n$.