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?
Dual cone and polar cone
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optimization
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1Are 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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1I am wondering if someone else already has defined such a thing for a purpose. – 2011-12-19
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1Very good question then, I am curious too. Would love to see an answer ; +1! – 2011-12-19
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1The 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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0@Fredrik, you mean to take real part of inner product of complex vectors? – 2011-12-19
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0@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