User:Sintel/Dual Weil-Euclidean norm: Difference between revisions
add note on dual bilinear form |
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$$ | $$ | ||
W = \begin{bmatrix} | W = \begin{bmatrix} | ||
\log_2 2 & 0 & \ | \log_2 2 & 0 & \cdots & 0 \\ | ||
0 & \log_2 3 & \ | 0 & \log_2 3 & \cdots & 0\\ | ||
\vdots & \vdots & \ddots & \vdots \\ | \vdots & \vdots & \ddots & \vdots \\ | ||
0 & 0 & \ | 0 & 0 & \cdots & \log_2 p | ||
\end{bmatrix} | \end{bmatrix} | ||
$$ | $$ | ||
And the row vector <math>j</math> containing the log-primes (aka the [[JIP]]): <math>j = \begin{bmatrix} | And the row vector <math>j</math> containing the log-primes (aka the [[JIP]]): <math>j = \begin{bmatrix} | ||
\log_2 2 & \log_2 3 & \ | \log_2 2 & \log_2 3 & \cdots & \log_2 p \\ | ||
\end{bmatrix} </math> | \end{bmatrix} </math> | ||
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Now let <math>l = \begin{bmatrix} | Now let <math>l = \begin{bmatrix} | ||
\frac{1}{\log_2 2} & \frac{1}{\log_2 3} & \ | \frac{1}{\log_2 2} & \frac{1}{\log_2 3} & \cdots & \frac{1}{\log_2 p} \\ | ||
\end{bmatrix} </math>, then | \end{bmatrix} </math>, then | ||