Majorization for the eigenvalues of Euclidean distance matrices

This paper investigates the relation between the eigenvalues of a Euclidean distance matrix (EDM) and those of the corresponding positive semidefinite matrix. More precisely, let D1 and D2 be two EDMs and let B1 and B2 be the corresponding positive semidefinite matrices such that Di=κ(Bi)(i=1,2). In this paper, when the eigenvalues of B1 majorizes those of B2, a condition under which the eigenvalues of D1 majorizes those of D2 is derived.