= Pseudotensor
Under an orthogonal coordinate transformation $R$, a Cartesian pseudotensor has the usual <tensor> transformation law multiplied by $\det R$. Thus proper <rotation matrices> act as on ordinary tensors, while an orientation-reversing change contributes an extra minus sign. Interpreted as a rank-three pseudotensor, the <Levi-Civita symbol> has the same numerical components in every orthonormal frame, because its ordinary three-index transformation already contributes a factor $\det R$.
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