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Minkowski Difference

Definition

Let $X$ be a vector space. Let $A,B\subseteq X$ then the Minkowski difference $A-^{.}B$ is given by

A-^{.}B:=\{x\in X:B+x\subseteq A\}=\bigcap _{b\in B}(A-b)

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Relation to Minkowski addition

The Minkowski difference is (in general) different then the Minkowski addition of a set and the negative of a set. That is, $A-B=\{a-b:a\in A,b\in B\}\neq A-^{.}B$ . Though if $B=\{b\}$ the two concepts coincide.

Let $X$ be a vector space. Let $A,B\subseteq X$ . Then

$B+(A-^{.}B)\subseteq A$

References

Definition

Relation to Minkowski addition

See also

References