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