# Sums of Subspaces

1. Sep 23, 2009

### bjgawp

If $$U_1, U_2, U_3,$$ are subspaces of V (over fields R and/or C), is the addition of the subspaces commutative and associative?

To me it seems rather trivial .. Since their summation is simply the set of all possible sums of the elements of $$U_1, U_2, U_3$$, and the elements themselves are associative and commutative, then so must be their subspaces and their sum.

Seems too easy to me ... I must be missing something ,,

2. Sep 24, 2009

### g_edgar

It is true. What you wrote is fine. But if you are doubtful, then you need to write it out more carefully.