= Solution
A second-order Cartesian <tensor> assigns components in each orthonormal coordinate system according to
$$
\boxed{T'_{ij}=R_{ik}R_{j\ell}T_{k\ell},\qquad T'=RTR^T,\qquad R^TR=I.}
$$
Here $R$ is the matrix taking old <vector> components to new ones, and repeated indices are summed. This is the <tensor component transformation law>; an arbitrary array of nine numbers is not a tensor unless its components in different frames obey this rule. No symmetry $T_{ij}=T_{ji}$ is implied by being a second-order tensor.
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