= Oriented-axis invariant Cartesian tensor
{title2=$T_{ij}=\alpha(\delta_{ij}-n_in_j)+\beta n_in_j+\omega\epsilon_{ijk}n_k$}
A <Cartesian second-rank tensor> invariant under all rotations about an oriented unit axis $n$ has the displayed form. A half-turn about the axis eliminates the mixed axial-transverse entries, and a quarter-turn makes the transverse block a scalar matrix plus an antisymmetric planar rotation generator. Conversely both transverse terms commute with every rotation about the axis. The antisymmetric term is allowed unless symmetry or an additional axis-reversing rotation is imposed. This differs from an <axially invariant second-rank tensor> for an unoriented axis.
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