= Antisymmetric contraction test for an antisymmetric tensor
If an array is antisymmetric in every <orthonormal basis> and its contractions with every <antisymmetric second-rank tensor> are invariant scalars, it obeys the <Cartesian second-rank tensor> transformation law. The difference $D=R^TA\prime R-A$ is antisymmetric and orthogonal to every antisymmetric test matrix. Choosing the test matrix equal to $D$ gives $D:D=0$, hence $D=0$. The <Frobenius inner product> is nondegenerate on the antisymmetric subspace.
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