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What is more compact equation of this relationship? $\sum |x_i|^2\sum |y_j|^2+\sum |x_j|^2\sum |y_i|^2-2|\sum x_i \overline y_i||\sum x_j \overline y_j|$

Remark: Euclidean space $\sum x_i^2\sum y_j^2+\sum x_j^2\sum y_i^2-2\sum x_i y_i\sum x_j y_j=\sum_i\sum_j(x_iy_j-x_jy_i)^2$

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Are you working in $\mathbb{C}^n$? –  Eric Stucky Dec 28 '12 at 15:02
    
@Stucky i am working on complex numbers –  Neo Dec 28 '12 at 15:42
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up vote 1 down vote accepted

$\sum_{i}^{n-1}\sum_{j=i+1}^{n}|(x_i\overline y_j-x_j\overline y_i)|^2$

i think it must be more compact equation of that relationship.

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