Euclidean distance matrix

In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. If A is a Euclidean distance matrix and the points are defined on m-dimensional space, then the elements of A are given by

where ||.||2 denotes the 2-norm on Rm.

Properties

Simply put, the element describes the square of the distance between the i th and j th points in the set. By the properties of the 2-norm (or indeed, Euclidean distance in general), the matrix A has the following properties.

See also

References

This article is issued from Wikipedia - version of the 7/12/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.