I read this article and am wondering why we can reconstruct Cartesian coordinates from a Gram matrix generated by taking dot product of the distance from the origin.
They had a Euclidean distance matrix. They generated a Gram matrix by $$G=-\frac12(D-1d_1^\top-d_11^\top).$$ Then, an eigenvalue decomposition is conducted on $G$ by $\Lambda_G=U_GGU_G^\top.$
Now, I don't understand why we can get the Cartesian coordinate by $\Lambda_G^{1/2}U_G^\top.$ Could anyone explain that simply?
