= Blindness of symmetric contraction tests to antisymmetric arrays
The <Frobenius inner product> of a symmetric <matrix> and an antisymmetric <matrix> is zero. Thus invariant contractions of an array with all <symmetric second-rank tensors> test only its symmetric part; an arbitrary basis-dependent antisymmetric part is invisible. A nonzero antisymmetric <matrix> in one basis and the zero <matrix> in another passes all such tests with scalar zero but is not a <Cartesian second-rank tensor>.
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