# Norm retrieval and phase retrieval by projections

## TL;DR

This paper provides a comprehensive analysis of norm retrieval, including classification theorems and examples, and establishes a new result on Parseval frames related to orthogonality of subspaces.

## Contribution

It offers new classification theorems for norm retrieval and a novel result on Parseval frames involving subspace orthogonality.

## Key findings

- Classification theorems for norm retrieval
- Examples illustrating the theory
- A new result on Parseval frames and subspace orthogonality

## Abstract

We make a detailed study of norm retrieval. We give several classification theorems for norm retrieval and give a large number of examples to go with the theory. One consequence is a new result about Parseval frames: If a Parseval frame is divided into two subsets with spans $W_1,W_2$ and $W_1 \cap W_2=\{0\}$, then $W_1 \perp W_2$.