On the equivalence between low rank matrix completion and tensor rank
Numerical Analysis
2015-01-13 v2
Abstract
The Rank Minimization Problem asks to find a matrix of lowest rank inside a linear variety of the space of n x n matrices. The Low Rank Matrix Completion problem asks to complete a partially filled matrix such that the resulting matrix has smallest possible rank. The Tensor Rank Problem asks to determine the rank of a tensor. We show that these three problems are equivalent: each one of the problems can be reduced to the other two.
Keywords
Cite
@article{arxiv.1406.0080,
title = {On the equivalence between low rank matrix completion and tensor rank},
author = {Harm Derksen},
journal= {arXiv preprint arXiv:1406.0080},
year = {2015}
}