User:Sintel/Dual Weil-Euclidean norm: Difference between revisions

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 == Generalized norm ==
-For some parameter <math>k</math>, set:
+For some parameter <math>k > 0</math>, set:
 $$
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 $$
-G^{-1}(k) = W^{-2} - \frac{k^2}{n+1} l^{\mathsf T}l
+G^{-1}(k) = W^{-2} - \frac{k^2}{nk^2+1} l^{\mathsf T}l
 $$
-And the relation to parametric badness is <math>E = \sqrt{\frac{n+1}{nk^2} - 1}</math> or <math>k = \sqrt{\frac{n+1}{n}(1+E^2)}</math>
+Which leads to a simple relation to <math>E</math>:
+$$
+nk^2E^2 = 1\\
+E = \sqrt{\frac{1}{nk^2}}\\
+k = \sqrt{\frac{1}{nE^2}}
+$$
 == References ==