Let P and Q be 2 orthogonal projectors. We prove that if Range(P) and Null(Q) are linearly independent, and Range(Q) and Null(P) are linearly independent, then $\displaystyle \left\| P-Q\right\|_{2} < 1$

Does Range(P) and Null(Q) are linearly independent mean that Range(P) $\displaystyle \cap $ Null(Q) $\displaystyle \neq \left\{0 \right\}$?

If yes, how do you use this fact to prove the problem?