Minkowski sum
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set
Analogously, the Minkowski difference (or geometric difference) is defined as
It is important to note that in general . For instance, in a one-dimensional case and the Minkowski difference , whereas The correct formula connecting Minkowski sum and difference is as follows (here stands for the complement of ):
![{\displaystyle A=[-2,2]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbb3b2c35beab902e541c06decf5cc3c5927108c)
![{\displaystyle B=[-1,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7fb6d50ed2578716b08499727541b3c1158b92cd)
![{\displaystyle A-B=[-1,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ceac3d392f986dc9d4e4bef20194c5474bf39cd)
![{\displaystyle A+(-B)=A+B=[-3,3].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cba8aaab0b445dad6fff3e8ecd62824f5f130203)
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