Positive-definite function: Difference between revisions

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m Examples: Corrected minor typo
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u^* A^{(g_y)} u
= \sum_{j, k = 1}^{n} \overline{u_k} u_j e^{i \langle y, x_k - x_j \rangle}
= \sum_{k = 1}^{n} \overline{u_k} u_j e^{i \langle y, x_k \rangle} \sum_{j = 1}^{n} u_j e^{- i \langle y, x_j \rangle}
= \left| \sum_{j = 1}^{n} \overline{u_j} e^{i \langle y, x_j \rangle} \right|^2
\ge 0.