Originally Posted by

**akolman** I'm stuck with two questions on vector subspaces and projections.

1. Let $\displaystyle V_1 $ and $\displaystyle V_2$ be subspaces of $\displaystyle \Omega$ and let $\displaystyle V_0 = V_1 \cap V_2$ Under what conditions $\displaystyle P_{V_0} =P_{V_1} P_{V_2}$

Well, for this one I see that it will work if one of $\displaystyle V_1 $ and $\displaystyle V_2 $ contains the other and also if $\displaystyle V_1 \perp V_2$ , but this doesn't seem like a good answer.

2. Let $\displaystyle V_1,V_2,V_3$ be subspaces. Does $\displaystyle V_1 \cap (V_2 + V_3) = V_1\cap V_2 + V_1\cap V_3$ in general? If not, does it hold if $\displaystyle V_2$ and $\displaystyle V_3$ are linearly independent?

Thanks in advance,