# On the Nuclear Norm and the Singular Value Decomposition of Tensors

arXiv: https://arxiv.org/abs/1308.3860 · HTML: https://mlsanity.com/paper/1308.3860/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2013.

## Built on by (most cited first, 2 of 2)

- [Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks](https://mlsanity.com/paper/2409.11772/) (2024)
- [Approximate Real Symmetric Tensor Rank](https://mlsanity.com/paper/2207.12529/) (2022)

## Abstract (arXiv)

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.