On the Nuclear Norm and the Singular Value Decomposition of Tensors
Optimization and Control
2014-04-23 v2 Numerical Analysis
Numerical Analysis
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1308.3860,
title = {On the Nuclear Norm and the Singular Value Decomposition of Tensors},
author = {Harm Derksen},
journal= {arXiv preprint arXiv:1308.3860},
year = {2014}
}