A projection on a vector space \(V\) is a linear operator \(P : V \rightarrow V\) such that \(P^2 = P\).
In linear algebra (a) and functional analysis (a), a projection is a linear transformation (a) \(P\) from a vector space (a) to itself (an endomorphism (a)) such that \(P \circ P = P\). That is, whenever \(P\) is applied twice to any vector, it gives the same result as if it were applied once (i.e. \(P\) is idempotent (a)). It leaves its image (a) unchanged.