On root frames in $\mathbb{R}^d$

TL;DR

This paper explores the properties of root frames in Euclidean spaces, showing they are a special subclass of scalable frames and introducing their relation to eigenframes, thus advancing understanding of structured frame systems.

Contribution

It establishes elementary properties of root frames, proves they are scalable, and connects them to the broader class of eigenframes, providing new insights into their structure.

Findings

Root frames are a subclass of scalable frames.

Root frames are examples of eigenframes.

Elementary properties of root frames are established.

Abstract

\emph{A root frame} for $\mathbb{R}^d$ is a finite frame whose vectors form a root system. In this note we establish some elementary properties of this class of frames and prove that root frames constitute a subclass of scalable frames. In addition, we show that root frames are examples of a larger class of frames called \emph{eigenframes}.