nLab
projector

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Idempotents

Contents

Idea

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

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

Vker(e)im(e). 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)