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If one alters a Euclidean space so that its inner product becomes negative in one or more directions, then the result is a pseudo-Euclidean space.
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If and Euclidean
If a relation is Euclidean and reflexive, it is also symmetric and transitive.
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If not stated otherwise, this article considers symmetry groups in Euclidean geometry, but the concept may also be studied in wider contexts ; see below.
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