The vectors do not have to be real, they can be from any space in which the inequality relation is defined.
Inequality of bargaining power | gender inequality | Wirtinger's inequality | Steffensen's inequality | Samuelson's inequality | Minkowski inequality | Inequality for All | Hölder's inequality | Hitchin–Thorpe inequality | Fisher's inequality | Economic inequality | Chebyshev's sum inequality | Cauchy's inequality | Cauchy–Schwarz inequality |