Tensor coordinate transformations: cosine matrix vs rotation matrix

Question

I have a tensor $\varepsilon(\vec r)$ and want to get $\varepsilon(\vec r')$. After some googling I've got confused, should cosine matrix to be used or coordinate transformation matrix? Some sources like this suggest to use $\varepsilon(\vec r')=Q\varepsilon(\vec r)Q^T$, where Q is a matrix of projections of the new basic vectors on the old ones.
While other sources, like the tensor Wikipedia page tell to use the coordinate transformation matrix $\varepsilon(\vec r')=R\varepsilon(\vec r)R^{-1}$.
Please, stop my suffering. Which way should I use to transform dielectric tensor in a simple Euclidean space?

Answer 1

You’ll find that both are equivalent, since the coordinate transformation/cosine matrices are orthogonal ($Q^T = Q^{-1}$).