  Euclidean distance matrices (EDM) are symmetric nonnegative matrices with
several interesting properties. In this article, we introduce a wider class of
matrices called generalized Euclidean distance matrices (GDMs) that include
EDMs. Each GDM is an entry-wise nonnegative matrix. A GDM is not symmetric
unless it is an EDM. By some new techniques, we show that many significant
results on Euclidean distance matrices can be extended to generalized Euclidean
distance matrices. These contain results about eigenvalues, inverse,
determinant, spectral radius, Moore-Penrose inverse and some majorization
inequalities. We finally give an application by constructing infinitely
divisible matrices using generalized Euclidean distance matrices.
