Minkowski addition
Sums vector sets A and B by adding each vector in A to each vector in B
Minkowski addition
In mathematics, the sumset of two subsets A and B of an (additive) abelian group is formed by adding each element of A to each element of B: A + B = { a + b ∣ a ∈ A , b ∈ B } . {\displaystyle A+B=\{a+b\mid a\in A,\ b\in B\}.} In geometry, the Minkowski sum of two subsets A and B of a Euclidean space is the set of the points whose position vectors form the sumset of the position vectors of A and B. The Minkowski sum depends on the choice of an origin in the Euclidean space. As a change of origin amounts to translate the Minkowski sum, the Minkowski sum is defined up to a translation, and its shape and orientation are well defined. The Minkowski difference (also Minkowski subtraction, Minkowski decomposition, or geometric difference) is the corresponding inverse, where (...
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