Tensor rank is not multiplicative under the tensor product

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Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen;
  • Related identifiers: doi: 10.1016/j.laa.2017.12.020
  • Subject: Computer Science - Computational Complexity | Mathematics - Commutative Algebra | 15A69 | Quantum Physics

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product... View more
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