Let K {\displaystyle {}K} be a field, V {\displaystyle {}V} a K {\displaystyle {}K} -vector space and U ⊆ V {\displaystyle {}U\subseteq V} a linear subspace. A linear mapping
is called a projection of V {\displaystyle {}V} onto U {\displaystyle {}U} , if U = Im φ {\displaystyle {}U=\operatorname {Im} \varphi } and φ | U = Id U {\displaystyle {}\varphi {|}_{U}=\operatorname {Id} _{U}} holds.
