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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on May 12, 2009
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(3):297-310; doi:10.1093/qjmam/hbp009
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Eigenvectors of a rotation matrix

Faiz Ahmad{dagger} and Riaz Ahmad Khan

( Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Rawalpindi, 46000, Pakistan )

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

Received 16 October 2008. Revise 4 December 2008. Accepted 20 March 2009.


  Abstract

If a tensor is invariant under rotation about a fixed axis, the matrices representing the tensor and the rotation commute with each other. The two matrices have common eigenvectors, therefore a knowledge of eigenvectors of the rotation matrix provides us with some information about eigenvectors of the tensor. This result is applied to derive familiar representations of a transversely isotropic tensor of rank 2 and the elasticity tensor possessing tetragonal symmetry. Representation of the elasticity tensor belonging to a particular symmetry class can be achieved in an elegant manner.


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