here. Any ideas for the second? What if (where is the full space) so that the LHS is but ? Can that happen?
I'm stuck with two questions on vector subspaces and projections.
1. Let and be subspaces of and let Under what conditions
Well, for this one I see that it will work if one of and contains the other and also if , but this doesn't seem like a good answer.
2. Let be subspaces. Does in general? If not, does it hold if and are linearly independent?
Thanks in advance,