Let V be an inner product space, let be an orthonormal subset of V. Prove that for any , we have
proof so far.
by a theorem, there exist unique vectors u in span(S) and v in the orthogonal complement of span(S) such that x = u + v.
Now, since u is orth. to v, meaning
Since , write
then
Since they are all orthogonal to one another, we can write
Now, I'm a bit stuck... Am I at least doing this right so far?