Euclidean space

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)