Theory of Computing Systems

, Volume 62, Issue 5, pp 1161–1174 | Cite as

The Complexity of Tensor Rank

  • Marcus Schaefer
  • Daniel Štefankovič


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 Håstad (J. Algorithm. 11(4), 644–654 1990). The hardness proof also implies an algebraic universality result.


Computational complexity Existential theory of fields Tensor rank 


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Authors and Affiliations

  1. 1.School of ComputingDePaul University ChicagoIllinoisUSA
  2. 2.Computer Science DepartmentUniversity of RochesterRochesterUSA

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