The G-stable rank for tensors

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.

24 pages

Cited by in corpus (2)

• A Gap in the Subrank of Tensors
• On rank in algebraic closure