# Euclidean space

From Encyclopedia of Mathematics

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

#### Comments

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

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

#### References

[a1] | M. Berger, "Geometry" , I , Springer (1987) |

**How to Cite This Entry:**

Euclidean space. E.D. Solomentsev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Euclidean_space&oldid=13577

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098