Positive cone

Summary

A positive cone in a real vector space is a subset closed under addition and under multiplication by nonnegative scalars. It must also contain no line through the origin. Positive cones are the same thing as compatible partial orders: the cone is the set of elements that are at least $0$. So one can describe an order on a vector space just by saying which vectors are positive. The same name is used for the set of nonnegative elements of an ordered group, ring or field.