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arXiv · 2608.21562

Border rank=rank for Kruskal tensors and a Kruskal's theorem for skew decompositions

Alexander Taveira Blomenhofer·Benjamin Lovitz
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Abstract

We show that border rank is equal to rank for Kruskal tensors. We also give an analogous Kruskal condition for alternating tensors, which certifies uniqueness of skew rank decompositions. Furthermore, we show that border skew rank is equal to skew rank for alternating Kruskal tensors, and we give an algorithm to find the minimum skew rank decomposition of alternating Kruskal tensors.

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Alexander Taveira Blomenhofer, Benjamin Lovitz. 2026-08-21. Border rank=rank for Kruskal tensors and a Kruskal's theorem for skew decompositions. https://arxiv.org/abs/2608.21562

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