projection of a vector

The projection of a vector onto the set F is given by .

The projection of a vector on a plane is its orthogonal projection on that plane.

In fact, the projections of a vector space are exactly the idempotent elements of the ring of linear transformations of the vector space.

In mathematics, the scalar projection of a vector on (or onto) a vector , also known as the scalar resolute or scalar component of in the direction of , is given by:

Since the notions of vector length and angle between vectors can be generalized to any n-dimensional inner product space, this is also true for the notions of orthogonal projection of a vector, projection of a vector onto another, and rejection of a vector from another.