Distance matrices and isometric embeddings

E. Bogomolny ¹, O. Bohigas ¹, C. Schmit ¹

Journal of Mathematical Physics, Analysis, Geometry 4 (2008) 7

We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one non-negative. Several generalizations are discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud