Orthogonal Projection #shorts

Finding the projection Px of x onto a linear space equipped with an orthonormal basis (u_1,...,u_k) is a linear combination of c_j u_j where c_j=u_j .x . This can be written as P=Q Q^T, were Q is the matrix containing the orthonormal basis as column vectors. The matrix Q satisfies Q^T Q=1. The cute formula P=Q Q^T will generalize to the case when the basis is no more orthonormal and become P=Q (Q^T Q)^(-1) Q^T in a later lecture.