5,322
edits
Line 145: | Line 145: | ||
&= \sum_k \sum_i \sum_j v_{i} \phi_k(\mathbf{x}^{(i)}) \phi_k(\mathbf{x}^{(j)})v_{j}\\ | &= \sum_k \sum_i \sum_j v_{i} \phi_k(\mathbf{x}^{(i)}) \phi_k(\mathbf{x}^{(j)})v_{j}\\ | ||
&= \sum_k \sum_i v_{i} \phi_k(\mathbf{x}^{(i)}) \sum_j \phi_k(\mathbf{x}^{(j)})v_{j}\\ | &= \sum_k \sum_i v_{i} \phi_k(\mathbf{x}^{(i)}) \sum_j \phi_k(\mathbf{x}^{(j)})v_{j}\\ | ||
&= \sum_k | &= \sum_k [\sum_i v_{i} \phi_k(\mathbf{x}^{(i)})]^2\\ | ||
&\geq 0 \quad | &\geq 0 \quad | ||
\end{aligned} | \end{aligned} |