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 $G$.

iffthe resulting Gram matrix is positive-definite. $\endgroup$