Moore–Penrose inverse of a Euclidean distance matrix

We obtain expressions for the Moore–Penrose inverse of a Euclidean distance matrix (EDM) that are determined only by the positive semidefinite matrix associated with the EDM. The results complement formulas for the Moore–Penrose inverse of an EDM given in Balaji and Bapat (2007) [2]. A formula for the inverse of a principal submatrix of an EDM is also derived, whose expression uses the Schur complement of the Laplacian of the EDM. As an application, we obtain an expression for the terminal Wiener index of a tree.