Advances in Applied Clifford Algebras

, Volume 11, Supplement 3, pp 41–48 | Cite as

Metric tensor Vs. Metric extensor

  • V. V. Fernández
  • A. M. Moya
  • W. A. Rodrigues


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.


Linearity Property Dual Basis Real Matrix Real Vector Space Linear Isomorphism 
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  1. [1]
    Fernáandez, V. V., Moya, A. M., and Rodrigues, W. A. Jr, Euclidean Clifford Algebra (paper I of a series of seven), this issue ofAACA 11 (S3) (2001).Google Scholar
  2. [2]
    Fernández, V. V., Moya, A. M., and Rodrigues, W. A. Jr., Extensors (paper II of a series of seven), this issue ofAACA 11 (S3) (2001).Google Scholar
  3. [3]
    Lasenby, A., Doran, C., and Gull, S., Gravity, Gauge Theories and Geometrical Algebras,Phil. Trans. R. Soc. 356, 4877–582 (1998).MathSciNetGoogle Scholar

Copyright information

© Birkhauser-Verlag AG 2001

Authors and Affiliations

  • V. V. Fernández
    • 1
  • A. M. Moya
    • 1
  • W. A. Rodrigues
    • 2
  1. 1.Institute of Mathematics, Statistics and Scientific ComputationIMECC-UNICAMPCampinasBrazil
  2. 2.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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