### Abstract

If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces.
We prove that if the distance matrix of a finite metric space is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points.

Original language | English |
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Publication date | 2008 |

Publication status | Published - 2008 |

Event | Workshop on Distance Geometry - Salzburg, Austria Duration: 5 May 2008 → 8 May 2008 |

### Workshop

Workshop | Workshop on Distance Geometry |
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Country | Austria |

City | Salzburg |

Period | 05/05/2008 → 08/05/2008 |

## Cite this

Hjorth, P. G. (2008).

*Finite Metric Spaces of Strictly negative Type*. Paper presented at Workshop on Distance Geometry, Salzburg, Austria.