If v is already orthogonal to w1, w2, and w3, its projection onto that subspace is just its projection onto w4. I don't know if that involves "calculating the inverse of " because I don't know what " " means for W a vector space.
W is the basis of the space. I was thinking to get the projection of v to W, I need to use . Could you please give a brief proof of "If v is already orthogonal to w1, w2, and w3, its projection onto that subspace is just its projection onto w4". Sorry for my ignorance. I am not a math guy.