# Definition:Minkowski Sum

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## 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:

- $A + B := \set {a + b: a \in A, b \in B}$

where the operation $+$ is vector addition.

The **Minkowski sum** is therefore a relation in the power set of $V$ in the sense that it is a mapping:

- $+: \powerset V^2 \to \powerset V$

## Source of Name

This entry was named for Hermann Minkowski.