Dual NormFor a given norm ![]() The above definition indeed corresponds to a norm: it is convex, as it is the pointwise maximum of convex (in fact, linear) functions By definition of the dual norm, ![]() This can be seen as a generalized version of the Cauchy-Schwartz inequality, which corresponds to the Euclidean norm. Examples:
![]() holds trivially, and is attained for
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