Metric tensor Vs. Metric extensor
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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 oftensors andextensors. 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 donot 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.
KeywordsLinearity Property Dual Basis Real Matrix Real Vector Space Linear Isomorphism
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