nLab
projector

Idea

In linear algebra a projector is a linear map $e:V\to V$ 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:

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

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

Related concepts

• projection