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arXiv · 2002.08435

The G-stable rank for tensors

Harm Derksen
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Abstract

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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Harm Derksen. 2020-02-19. The G-stable rank for tensors. https://doi.org/10.2140/ant.2022.16.1071

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