On (super-)spherical distance matrices and two results from Schoenberg

被引：4

作者：

Critchley, F ^{[1
]}

Fichet, B ^{[1
]}

机构：

[1] UNIV AIX MARSEILLE 2,LAB BIOMATH,F-13385 MARSEILLE,FRANCE

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1997年 / 251卷

关键词：

D O I：

10.1016/0024-3795(95)00558-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new characterization of simplicial distance matrices is obtained. The superspherical semidistance matrices are introduced. Two results deriving from Schoenberg are studied. A short proof of the first is obtained, before strengthening it to show that every circum-Euclidean semidistance matrix is superspherical. The second, that L(2) embeds in L(1), required a very sophisticated proof. The relationship between(super-) spherical and Euclidean matrices is clarified and, in the finite case, leads to an elementary proof of this second result. Finally, the classes of matrices studied here are located in the wider context of the classes studied by Critchley and Fichet (1994). (C) Elsevier Science Inc., 1997

引用

页码：145 / 165

页数：21