Euclidean Space

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Related to Euclidean vector: magnitude, Euclidean vector space

euclidean space

[yü′klid·ē·ən ′spās]
(mathematics)
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 ?
The distance distribution for the images is much different than the one for Euclidean vectors.
Figure 9 shows the performance results for 10-dimensional uniformly distributed Euclidean vectors.
For Euclidean vectors generated in clusters, we use two different query sets.
2] with Respect to Different Query Ranges (for Euclidean vectors generated in clusters)
In these experiments, the same sets of Euclidean vectors are used as in Section 5, where in the first set the vectors are generated randomly, and in the second set the vectors are generated in clusters.
For example, for the structure mvpt(m = 2, v = 1, k = 13, p = 7), for a set of 50,000 Euclidean vectors, there are 12 vantage points along any path from the root to a leaf, since [[log.
Again, performance results are obtained for both data sets of Euclidean vectors, and are as in Figures 19-21.
Similar behavior is also observed for the experiments with Euclidean vectors generated in clusters.