Minkowski addition

Summary

The Minkowski sum of two subsets $A$ and $B$ of a vector space is the set $A + B$ of all sums $a + b$ with $a \in A$ and $b \in B$. Together with scaling $\lambda A = \set{\lambda a : a \in A}$, it makes the convex bodies of $\R^n$ into a cone-like algebraic structure. Volume behaves well under this addition, which leads to the Brunn–Minkowski inequality and the theory of mixed volumes.