Euclidean distance matrix

A Euclidean distance matrix (EDM) is a real m×m matrix X such that for some points y1,,ym in m, Xik=yi-yk22, where 2 is the 2-norm on m.

A EDM X inherits the following from the norm that defines it:

  • Xii=0;

  • Xij=Xji0;

  • XikXij+Xjk.

Additionally, X is a EDM if and only if the diagonal entries of X are all 0 and for all zm whose componentsPlanetmathPlanetmathPlanetmath sum to 0, zTXz0.

Finally, the set of m×m EDMs forms a convex cone ( in the set of all m×m matrices.


  • 1 S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
Title Euclidean distance matrix
Canonical name EuclideanDistanceMatrix
Date of creation 2013-03-22 14:37:15
Last modified on 2013-03-22 14:37:15
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 7
Author mathcam (2727)
Entry type Definition
Classification msc 15A48