Definition:Minkowski Sum

From ProofWiki
Jump to navigation Jump to search

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.