Inverse eigenvalue problem of distance matrix via orthogonal matrix

In this paper, for a given list σ   of real numbers λ1,λ2,…,λnλ1,λ2,…,λn, with sum zero and some additional more technical conditions specified in the paper, we construct a Euclidean distance matrix (EDM) having σ as its list of eigenvalues, without using Hadamard matrices.