The Complexity of Tensor Rank

Marcus Schaefer; Daniel Stefankovic

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arXiv · 1612.04338

The Complexity of Tensor Rank

Marcus Schaefer·Daniel Stefankovic

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Abstract

We show that determining the rank of a tensor over a field has the same complexity as deciding the existential theory of that field. This implies earlier NP-hardness results by H{\aa}stad~\cite{H90}. The hardness proof also implies an algebraic universality result.

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Marcus Schaefer, Daniel Stefankovic. 2016-12-13. The Complexity of Tensor Rank. https://arxiv.org/abs/1612.04338

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