= Cartesian second-rank tensor
{c}
{title2=$T\prime=RTR^T$}
= Cartesian rank-two tensor
{c}
{synonym}
A Cartesian second-rank tensor has component matrix $T$ in each <orthonormal basis>, with transformation $T\prime=RTR^T$ under an orthogonal component change $R$. Both indices transform; this is why assigning arbitrary matrices independently in different bases does not define a <tensor>. The <determinant>, <trace>, and <Frobenius inner product> with another such tensor are unchanged by these basis transformations.
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