# nLab projector

### Context

#### Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

# Contents

## Idea

In linear algebra a projector is a linear map $e \colon V \to V$ that “squares to itself” in that its composition with itself is again itself: $e \circ e = e$.

A projector $e$ leads to a decomposition of the vector space $V$ that it acts on into a direct sum of its kernel and its image:

$V \simeq ker(e) \oplus im(e) \,.$

The notion of projector is the special case of that of idempotent morphism.

Revised on September 26, 2013 13:47:12 by Toby Bartels (98.23.150.36)