Stretching maps for tensors

TL;DR

This paper introduces a generalized stretching map for even-order square tensors that preserves algebraic properties, enables tensor representation as matrices, and offers potential for data compression through noninjective mappings.

Contribution

It proposes a novel, generalized stretching map for tensors that relaxes injectivity, allowing for symmetry properties and data compression applications.

Findings

Stretching map preserves algebraic tensor properties.

Noninjective stretching maps can average tensors.

Potential for tensor data compression.

Abstract

We consider an algebra of even-order square tensors and introduce a stretching map which allows us to represent tensors as matrices. The stretching map could be understood as a generalized matricization. It conserves algebraic properties of the tensors. In the same time, we don't necessarily assume injectivity of the stretching map. Dropping the injectivity condition allows us to construct examples of stretching maps with additional symmetry properties. Furthermore, the noninjectivity leads to the averaging of the tensor and possibly could be used to compress the data.