Don't be confused with orthographic projection

orthographic are perspective projection are ways to transform 3d scene into a 2d surface.

Definition

Given an n-dimensional vector space and a p-dimensional subspace of , and being an orthonormal basis for . Let be a vector in , the orthogonal projection of onto is given by

When we are doing orthogonal projection, we throw away the part of the vector that are not part of the subspace. Say if is an orthonormal basis for and , then the projection will drop all the terms with vectors not part of orthonormal basis of ()