Orthogonal Projection onto a Subspace
- Let P be an orthogonal projection matrix, then and .
- x and y are two vectors. The projection of y onto x is .
New question: Let . y is an vector. What is the projection of y onto the column space of A?
Proof: it is the same to find x to minimize which is a least squares problem. As we know, the answer is . Then the projection is . Hence the projector is .