The geometry of rank decompositions of matrix multiplication I: 2x2 matrices

Luca Chiantini; Christian Ikenmeyer; J. M. Landsberg; Giorgio Ottaviani

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arXiv · 1610.08364

The geometry of rank decompositions of matrix multiplication I: 2x2 matrices

Luca Chiantini·Christian Ikenmeyer·J. M. Landsberg·Giorgio Ottaviani

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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.

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Luca Chiantini, Christian Ikenmeyer, J. M. Landsberg, Giorgio Ottaviani. 2016-10-25. The geometry of rank decompositions of matrix multiplication I: 2x2 matrices. https://arxiv.org/abs/1610.08364

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