Axially invariant second-rank tensor
= Axially invariant second-rank tensor
{title2=$T=\alpha I+\beta nn^T$}
A <Cartesian second-rank tensor> invariant under every proper rotation preserving an unoriented axis $n$ has this form. Rotations about the axis give a planar block $aI+bJ$ and eliminate mixed axial-planar entries. A half-turn about a transverse axis reverses $J$, forcing $b=0$. If only rotations about the oriented axis are imposed, this planar antisymmetric term may survive.