On the Nuclear Norm and the Singular Value Decomposition of Tensors

  title={On the Nuclear Norm and the Singular Value Decomposition of Tensors},
  author={Harm Derksen},
  journal={Foundations of Computational Mathematics},
  • H. Derksen
  • Published 18 August 2013
  • Mathematics, Computer Science
  • Foundations of Computational Mathematics
Finding the rank of a tensor is a problem that has many applications. Unfortunately, it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of the rank of a tensor. We determine the nuclear norm of various tensors of interest. Along the way, we also do a systematic study various measures of orthogonality in tensor product spaces and we give a new generalization of the singular value decomposition… 

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