Correlation Minimizing Frames in Small Dimensions

TL;DR

This paper investigates correlation minimizing frames in small dimensions, especially in three dimensions, aiming to identify frames that are as close to orthogonal as possible by minimizing maximal inner products.

Contribution

It initiates a systematic cataloging of correlation minimizing frames in small dimensions, focusing on the case d=3, and advances understanding of their structure.

Findings

Identified candidate correlation minimizing frames in three dimensions.

Provided initial classification and properties of these frames.

Set groundwork for further exploration of frames in small dimensions.

Abstract

A uniform tight frame of N vectors for a d dimensional space is correlation minimizing if among all such frames it is as "nearly" orthogonal as possible, i.e., it minimizes the maximal inner product of unequal vectors. In this paper we begin to catalog these frames for small dimensions, in particular, d=3.