Euclidean Space

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Related to N-dimensional Euclidean space: Euclidean vector space

euclidean space

[yü′klid·ē·ən ′spās]
A space consisting of all ordered sets (x1, …, xn ) of n numbers with the distance between (x1, …, xn ) and (y1, …, yn ) being given by the number n is called the dimension of the space.

Euclidean Space


in mathematics, a space whose properties are described by the axioms of Euclidean geometry. In a more general sense, a Euclidean space is an n-dimensional vector space, into which several special Cartesian coordinates can be introduced so that its metric is defined in the following manner: If point M has the coordinates (x1x2, …, xn and point M* has the coordinates (x1*, x2*, …, xn*), then the distance between these points is

References in periodicals archive ?
Atomic objects are real-valued vectors in n-dimensional Euclidean space, in practice represented by n-tuples of components taken in some basis.
The setting for this paper is n-dimensional Euclidean space [R.
n] is contained in the n-dimensional Euclidean space