I'm struggling with a problem with tensor notation.
we assume that a stiffness tensor $C_{ijkl}$ has been measured relative to a Cartesian coordinate system with unit base vectors $e_1$, $e_2$, and $e_3$. If the same material is considered, but the stiffness matrix is measured relative another Cartesian coordinate system with unit base vectors $e’_1$, $e’_2$, and $e’_3$, generally the components of the stiffness tensor will change to $C’_{ijkl}$. Derive $C’_{ijkl}$ corresponding to Eq. (5.13) in the text book using tensors and the general relations between a tensors components in two different coordinate systems: $v’_i = l_{ij} v_{j}$ and $v_i = l’_{ij}v’_j$ where $l_{ij} = e’_i \cdot e_j$ and $l’_{ij} = e_i \cdot e’_j$.
The form I am supposed to write is $C’_{ijkl} = l_{ij} C_{ijkl} \cdot l_{ji}$ but that doesn't work ! Please help!