Metric Tensor Vs. Metric Extensor

Details Metric Tensor Vs. Metric Extensor Metric Tensor Vs. Metric Extensor

2002-12-16

arxiv.org/abs/math-ph/0212048v2

Advances in Applied Clifford Algebras 11(S3),41-48 (2001)

Physics

Mathematical Physics

Scientific paper

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.

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