Decomposing Tensors into Frames

TL;DR

This paper investigates the structure of symmetric tensors that decompose into a small set of vectors forming a unit norm tight frame, exploring their geometric and algebraic properties.

Contribution

It characterizes the variety of symmetric tensors decomposable into unit norm tight frames, linking tensor decomposition with frame theory.

Findings

Identifies conditions under which tensors decompose into unit norm tight frames

Provides a geometric description of the tensor variety associated with frames

Establishes connections between tensor rank and frame properties

Abstract

A symmetric tensor of small rank decomposes into a configuration of only few vectors. We study the variety of tensors for which this configuration is a unit norm tight frame.