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Dual cone and polar cone http://en.wikipedia.org/wiki/Dual_cone_and_polar_cone are defined only on $\mathbb R^n$. Has anyone seen the extension to $\mathbb C^n$? Any references for these?

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    Are you just wondering or you're asking if someone else already has defined such a thing for a purpose? Because there is probably a way to define such a generalization but I've never heard of a purpose for it, though.2011-12-18
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    I am wondering if someone else already has defined such a thing for a purpose.2011-12-19
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    Very good question then, I am curious too. Would love to see an answer ; +1!2011-12-19
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    The definition on Wikipedia automatically generalizes to any inner product space (and $\mathbb{C}$ has of course an inner product)2011-12-19
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    @Fredrik, you mean to take real part of inner product of complex vectors?2011-12-19
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    @Sunni: If $z_1=a_1+ib_1$ and $z_2=a_2+ib_2$, then we define $z_1 \cdot z_2 = a_1 a_2+b_1b_2$. You can check that this gives the absolute value squared when $z_1=z_2$.2011-12-19

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