This should be easy, I'm not sure what I'm missing!! Any help would be great...
Let W be a finite dim subspace of an inner product space V. Show a projection, on along such that the nullspace of T, .
What I know:
So far, I know that by a theorem, there are unique vectors such that
I know by definition is a projection on W along if for with , we have
Finally, I know if x and y are orthogonal vectors, that
It seems like it should fall into place so easily... I just don't know how to define my T function so it works for each case and still lands me in the complement of W. Please help!!