My favorite thing about convex hulls is their link to linear algebra. For two vectors u and v in R^n, v is majorized by u if and only if v is in the convex hull

My favorite thing about convex hulls is their link to linear algebra. For two vectors u and v in R^n, v is majorized by u if and only if v is in the convex hull of all vectors generated by permitting the coordinates of u.