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 x 1 , x 2 , … , x n {displaystyle x_{1},x_{2},ldots ,x_{n}} are defined on m-dimensional space, then the elements of A are given by 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 x 1 , x 2 , … , x n {displaystyle x_{1},x_{2},ldots ,x_{n}} are defined on m-dimensional space, then the elements of A are given by where ||.||2 denotes the 2-norm on Rm. Simply put, the element a i j {displaystyle a_{ij}} 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.