Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
1  
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. –  Patrick Da Silva Dec 18 '11 at 23:53
1  
I am wondering if someone else already has defined such a thing for a purpose. –  Sunni Dec 19 '11 at 0:18
1  
Very good question then, I am curious too. Would love to see an answer ; +1! –  Patrick Da Silva Dec 19 '11 at 0:25
1  
The definition on Wikipedia automatically generalizes to any inner product space (and $\mathbb{C}$ has of course an inner product) –  Fredrik Meyer Dec 19 '11 at 6:04
    
@Fredrik, you mean to take real part of inner product of complex vectors? –  Sunni Dec 19 '11 at 15:28
show 1 more comment

1 Answer

As I see it, the definition in Wikipedia is for any Linear Space. The book by Aliprantis and Border defines polars for any Dual Set, which is even more general. These general definitions are very useful in Convex Optimization, but I've never seen it used on $\mathbb{C}^n$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.