Étude des puissances d’une distance. (Study of the power of a distance). (French. English summary) Zbl 0636.62060
Summary: The aim of this paper is to gather some old and new results on the properties of the power of a distance. The problem of the existence of a Euclidean representation for such a power distance is emphasized. A generalization of Schur’s lemma on the Hadamard product of matrices is given, the last section being devoted to applications, in data analysis, of this results.
MSC:
62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
62H99 | Multivariate analysis |
15B48 | Positive matrices and their generalizations; cones of matrices |
15B57 | Hermitian, skew-Hermitian, and related matrices |
15A63 | Quadratic and bilinear forms, inner products |