The G-stable rank for tensors

Understand

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.