Projection

If $$A$$ is skinny and full rank, then the projection operation is $$\mathcal P_{\mathcal R(A)}(y) = A(A^TA)^{-1}A^T y$$

Properties of projection matrix $$P$$
TBC
 * If $$P$$ is a projection matrix, then so is $$I-P$$.
 * The norm of a projection matrix is either 1 or 0 either 1 or 0