An inequality for the distances between finitely many points on a hypersphere (Q1825434)

The author discusses squared distance matrices in \(E^ n\). He obtains an inequality for the distances between a finite point set on a hypersphere, containing their squared distances and a constant which depends only on the dimension. It becomes an equality iff all the negative eigenvalues of the squared distance matrix A of the point set are equal. The proof uses assertions about the eigenvalues of A. Then he gives corollaries for special point sets on a hypersphere and for geodesic distances of a point set in a spherical space.