Namespaces
Variants
Actions

Euclidean space

From Encyclopedia of Mathematics
Revision as of 17:04, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euclidean_space&oldid=38673
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article