User:Tokenzero/sandbox/definite
where CD is the Cayley-Menger determinant.[1]
- embeds isometrically in Hilbert space L2 iff it embeds in Rn for some n
- " any finite metric space can be embedded into a finite-dimensional L∞ space with no distortion. Simply map each of the n points of the metric space to the n-dimensional vector of distances from all points."
- Distance geometry -> Cayley–Menger_determinant
- The only examples that need n+3 have n+3 points: A MENGER REDUX: EMBEDDING METRIC SPACES ISOMETRICALLY IN EUCLIDEAN SPACE.
- For exact embeddings: Geometry and Cuts
- For approximate embeddings: Matousek
- For a non-matrix view of linear algebra and statements that work for general fields and rings Serge Lang
- For functional analysis: here.
- Applications of semidefinite programming: Anthony Man-Cho So
- For centroid: here
- ^ Maehara, Hiroshi (2013). "Euclidean embeddings of finite metric spaces". Discrete Mathematics. 313 (23): 2848–2856. doi:10.1016/j.disc.2013.08.029. ISSN 0012-365X. Theorem 2.6