\displaystyle  \left( \sum_{i=1}^n w_i |\langle u, v_i \rangle_{H}|^2\right)^{1/2} \leq \|u \|_{H} \left( \sup_{1 \leq i \leq n} \sum_{j=1}^n w_j |\langle v_i, v_j\rangle_{H}| \right)^{1/2}. \ \ \ \ \ (13)