Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The G-stable rank for tensors   We introduce the $G$-stable rank of a higher order tensors over perfect
fields.
  The $G$-stable rank is related to the Hilbert-Mumford criterion for stability
in Geometric Invariant Theory. We will relate the $G$-stable rank to the tensor
rank and slice rank. For numerical applications, we express the $G$-stable rank
as a solution to an optimization problem. Over the field ${\mathbb F}_3$ we
discuss an application to the Cap Set Problem.

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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th