Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of rank decompositions of matrix multiplication I: 2x2
  matrices   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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The categories of this paper are: astro-ph
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The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat