Euclidean group

The Euclidean group $E (𝑛)$ is the isometry group of $𝑛$ -dimensional Euclidean space $𝔼 𝑛$ , #m/def/geo/affine consisting of transformations that preserve Euclidean distance. It is equivalent to the semidirect product of the appropriate real orthogonal group with the translation group

E (𝑛) = O (𝑛) ⋊ ℝ 𝑛

The relativistic counterpart is the Poincaré group

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Euclidean group

Related groups