I have distance matrix $D$ that was calculated by some distance (non-Euclidean but satisfying distance requirements). Is there a set of points in some Euclidean space such that it generates matrix of Euclidean distances that is equal $D$?


I know that if $G=-HDH/2$ is p.d. where H is the centering matrix then such embedding exists. However, I don't have any information about $G$.



Given a distance matrix is there an isometric embedding?
No. The magic words are [Cayley-Menger](http://mathworld.wolfram.com/Cayley-MengerDeterminant.html), but an explicit answer is given [here.](https://mathoverflow.net/questions/12394/representability-of-finite-metric-spaces)


