Rotation invariance of the Levi-Civita symbol
= Rotation invariance of the Levi-Civita symbol
{title2=$R_{ia}R_{jb}R_{kc}\epsilon_{abc}=(\det R)\epsilon_{ijk}$}
The <determinant> transformation formula for the <Levi-Civita symbol> shows that it is invariant under every proper <rotation matrix>, for which $\det R=1$. Under an orthogonal reflection its sign reverses. This distinguishes proper-rotation isotropy from the <pseudotensor> transformation convention when both orientations are included.