Let be a subspace of and a compliment of . An matrix A is said to be a projector into along if , is the projection of into along
Let be a projector into along T
So, elements of are solutions of a system of finitely many hyper planes passing through origin
The following are equivalent For a matrix A i) A is a projectore ii) ie, is an idempotent iii) iv) v) is a direct sum
Proof. Let be a basis of and of T
if
let ie,
A is the projection of along □