On the Nuclear Norm and the Singular Value Decomposition of Tensors

Harm Derksen

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arXiv · 1308.3860

On the Nuclear Norm and the Singular Value Decomposition of Tensors

Harm Derksen

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Abstract

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 to higher order tensors.

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BibTeX RIS

Harm Derksen. 2014-04-21. On the Nuclear Norm and the Singular Value Decomposition of Tensors. https://arxiv.org/abs/1308.3860

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