Proving the inequality below.
Based on $ i \neq \tilde{i} $, for all $k$, we have the inequality that:
$ \langle P_{i\cdot},P_{k\cdot}\rangle - \langle P_{\tilde{i}\cdot},P_{k\cdot}\rangle \le \|P_{i\cdot}-P_{\tilde{i}\cdot}\|_2\ \|P_{k\cdot}\|_2 $
where $P_{i\cdot}$ means the $i$ row of the matrix $P$.
Can anyone help me on this, I have no clue to prove it.