标题： 度量张量 对比 度量外延 显示英文标题

标题： Metric Tensor Vs. Metric Extensor

摘要： In this paper we give a comparison between the formulation of the concept of metric for a real vector space of finite dimension in terms of \emph{张量} and \emph{张量积}. A nice property of metric extensors is that they have inverses which are also themselves metric extensors. This property is not shared by metric tensors because tensors do \emph{不，不是} have inverses. We relate the definition of determinant of a metric extensor with the classical determinant of the corresponding matrix associated to the metric tensor in a given vector basis. Previous identifications of these concepts are equivocated. The use of metric extensor permits sophisticated calculations without the introduction of matrix representations. 显示英文摘要

摘要： In this paper we give a comparison between the formulation of the concept of metric for a real vector space of finite dimension in terms of \emph{tensors} and \emph{extensors}. A nice property of metric extensors is that they have inverses which are also themselves metric extensors. This property is not shared by metric tensors because tensors do \emph{not} have inverses. We relate the definition of determinant of a metric extensor with the classical determinant of the corresponding matrix associated to the metric tensor in a given vector basis. Previous identifications of these concepts are equivocated. The use of metric extensor permits sophisticated calculations without the introduction of matrix representations.