Abstract
We introduce the -stable rank of a higher order tensors over perfect fields. The -stable rank is related to the Hilbert–Mumford criterion for stability in geometric invariant theory. We will relate the -stable rank to the tensor rank and slice rank. For numerical applications, we express the -stable rank as a solution to an optimization problem. Over the field we discuss an application to the cap set problem.
Citation
Harm Derksen. "The -stable rank for tensors and the cap set problem." Algebra Number Theory 16 (5) 1071 - 1097, 2022. https://doi.org/10.2140/ant.2022.16.1071
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