Faiz Ahmad
Abstract
General methods are applied to find complete sets of invariants of a tensor of rank 3. When the results are specialized to the piezoelectric tensor, it is found that the tensor has no linear invariant. Also under SO(2), as well as SO(3), the piezoelectric tensor has five quadratic invariants. The sets of invariants are complete.
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General methods are applied to find complete sets of invariants of a tensor of rank 3. When the results are specialized to the piezoelectric tensor, it is found that the tensor has no linear invariant. Also under SO(2), as well as SO(3), the piezoelectric tensor has five quadratic invariants. The sets of invariants are complete.
Key concepts: Cartesian tensor, Tensor (intrinsic definition), Invariants of tensors, Invariant (physics), Rank (graph theory), Mathematics, Tensor density, Symmetric tensor