Eigenvalue properties of gram matrices associated with simplexes and polygons
摘要
The eigenvalues of the Gram matrices of simplices in Euclidean, hyperbolic, and spherical geometries are investigated. Refined properties of the eigenvalues are derived for Gram matrices associated with Euclidean, hyperbolic, and spherical triangles. The study extends to a related matrix for Euclidean polygons, providing a detailed analysis of its eigenvalues.