Euclidean space

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A space the properties of which are described by the axioms of Euclidean geometry. In a more general sense, a Euclidean space is a finite-dimensional real vector space with an inner product , , which in a suitably chosen (Cartesian) coordinate system

is given by the formula


Sometimes the phrase "Euclidean space" stands for the case , as opposed to the case — Euclidean plane.

See, e.g., [a1], Chapts. 8, 9.


[a1] M. Berger, "Geometry" , I , Springer (1987)
How to Cite This Entry:
Euclidean space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article