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,
.
Then show
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!!