Definition:Minkowski Sum

Definition
Let $\mathcal X$ be a vector space.

Let $A, B$ be two subsets of $\mathcal X$.

Then the Minkowski sum of $A$ and $B$, denoted as $A + B$, is defined as:


 * $A + B := \left\{{a + b: a \in A, b \in B}\right\}$

The Minkowski sum is therefore a binary relation in the power set of $\mathcal X$ in the sense that it is a mapping:
 * $+ : \mathcal P \left({\mathcal X}\right)^2 \to \mathcal P \left({\mathcal X}\right)$