# Definition:Minkowski Sum

## Definition

Let $V$ be a vector space.

Let $A, B$ be two subsets of $V$.

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 relation in the power set of $V$ in the sense that it is a mapping:

$+ : \mathcal P \left({V}\right)^2 \to \mathcal P \left({V}\right)$

## Source of Name

This entry was named for Hermann Minkowski.