Factorizations of linear relations by idempotents

TL;DR

This paper investigates how linear relations can be expressed as products of idempotent relations, extending existing operator factorization results to a broader context.

Contribution

It provides new characterizations of linear relations that can be factorized into idempotents, generalizing known operator factorizations.

Findings

Characterizations of linear relations factorable by idempotents

Extension of operator factorization results to linear relations

Broader understanding of linear relation structures

Abstract

We study the class of those linear relations that can be factorized as products of idempotent relations. We provide several characterizations of this class, extending known factorization results for operators to the more general setting of linear relations.