Euclidean Distance Geometry

Source: doi:10.2307/1968654 Authors: Egor Lyfar Status: verified Main declarations: DistanceGeometry.schoenberg, DistanceGeometry.trilateration_le_two Tags: distance-geometry, euclidean-geometry, linear-algebra, cayley-menger MSC: 51K05, 52C99, 15A18

This project develops three parts of finite Euclidean distance geometry: both directions of Schoenberg's basepoint-centered Gram characterization with a rank-controlled positive-semidefinite factorization, a codimension-one trilateration bound, and the Cayley--Menger determinant through the segment and triangle cases, including the triangle-area identity underlying Heron's formula.