Generalized Euclidean distance matrices
R. Balaji, R.B. Bapat, Shivani Goel · Linear and Multilinear Algebra · 2021
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 (GEDMs) that include EDMs. Each GEDM is an entry-wise nonnegative matrix. A GEDM 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.