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Engineering LibreTexts

14: Appendix C- Isotropic Tensors

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  • Isotropic tensors play a fundamental role in tensor algebra as well as in fluid mechanics. We can easily test whether or not a given tensor is isotropic, but is there a way to identify all isotropic tensors?

    Because an isotropic tensor is invariant under under every rotation, it must in particular be invariant under very slight rotations. In the limit of an infinitesimal rotation, the rotation matrix is just the identity plus a small added matrix. This allows us to simplify the algebra needed to derive requirements for isotropy.

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