research product . Other ORP type . 2017

Tensor rank is not multiplicative under the tensor product

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen;
Closed Access English
  • Published: 25 May 2017
  • Country: Netherlands
Abstract
textabstractThe tensor rank of a tensor is the smallest number r such that the tensor 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 (not to be confused with the "tensor Kronecker product" used in algebraic complexity theory, which multiplies two k-tensors to get a k-tensor). Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. It is well-known that tensor rank is not in general multiplicative under the tensor Kronecker product. A result of our study is that tensor rank is also not in general mu...
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Other ORP type . 2017
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