Bounds on the tensor rank

TL;DR

This paper introduces a new criterion for establishing lower bounds on the cactus rank of tensors and refines it to identify minimal, unique tensor decompositions.

Contribution

It provides a novel sufficient criterion for lower bounds on cactus rank and refines conditions for minimal, unique tensor decompositions.

Findings

Established a sufficient criterion for cactus rank lower bounds.

Refined the criterion to identify minimal, unique tensor decompositions.

Provided explicit conditions for non-redundant tensor decompositions.

Abstract

We give a sufficient criterion for a lower bound of the cactus rank of a tensor. Then we refine that criterion in order to be able to give an explicit sufficient condition for a non-redundant decomposition of a tensor to be minimal and unique.