论文标题
G-Stable张量排名
The G-stable rank for tensors
论文作者
论文摘要
我们介绍了$ g $稳定的高级张量量的排名。 $ g $稳定的等级与几何不变理论中的稳定性标准有关。我们将将$ g $稳定的排名与张量排名和切片等级联系起来。对于数值应用程序，我们将$ G $稳定的等级表示作为解决优化问题的解决方案。在字段上$ {\ mathbb f} _3 $我们讨论了CAP集问题的应用程序。
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.
