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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on October 26, 2008
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(1):31-38; doi:10.1093/qjmam/hbn021
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© The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Linear invariants of a Cartesian tensor

Faiz Ahmad{dagger} and Muneer Ahmad Rashid

( Center for Advanced Mathematics and Physics, National University of Sciences and Technology, Electrical and Mechanical Engineering College, Peshawar Road, Rawalpindi, Pakistan )

{dagger} <faizmath{at}hotmail.com>

Received 12 May 2008. Revise 18 September 2008.
  Abstract

The number of linear invariants under SO(3) as well as SO(2) of a Cartesian tensor of an arbitrary rank is studied. A linear form is defined in terms of elements of a tensor. It is established that the number of linear invariants of a tensor of rank n under SO(3) equals the dimension of the space of isotropic tensors of rank n. Formulas for the number of invariants in the two cases are also derived. For the elasticity tensor, our analysis confirms the results of Norris.


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