Thanks for trying to help, I think I've figured it out though:
The definition of addition among subspaces follows this definition:
U+U = {a+b, such that aЄU and bЄU}.
Since U is a subspace, addition is closed in U, so adding two elements in U would simply produce another element in U...
What exactly is the "addition of subspaces?" It is obviously not the same as the "union of subspaces," since the union of subspaces A and B in V is a subspace of V only if A is contained in B (or B is contained in A).
1. Suppose that U is a subspace of V. What is U+U?
2. Homework Equations :
There's a theorem that states: Suppose that A and B are subspaces of V. Then V is the direct sum of A and B (written as A [plus with a circle around it] B) if and only if: 1) V=A+B (meaning, the two...