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

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons202366

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

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Volltexte (frei zugänglich)

arXiv:1610.08364.pdf
(Preprint), 162KB

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Zitation

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.


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