
Re: Generalizing Orthogonal Projection
Posted:
Jan 22, 2013 1:05 AM


On Mon, 21 Jan 2013, hbertaz@gmail.com wrote:
> Say we have a 1D subspace L (i.e., a line thru the origin) in R^3 , and > let q=(x,y,z) be a point in R^3 which is not on the line. Then I don't see > how to project q orthogonally onto L; I can see how to project q into a > 2D subspace P : the projection of q into P is the ortho complement, and > every vector in P is in the orthogonal complement of the ortho projected > line. But, the same is not the case with q and L. Sorry for the rambling; > my question is then actually: > > If L is a 1D subspace of R^3, and q=(x,y,z) is a point not on L. Can we > define the orthogonal projection of q into L, or do we need to have a plane > P (as subspace) , to define an ortho projection of q?
Yes, the orthogonal projection of q onto L, is the orthogonal projection of q onto L within the plain determined by q and L.

