In a book I found the following expression:
$\int_V (A_{ij} \delta B_{ij}) dV = \int_S (T_i \delta c_i) dS $
That apparently is equal to:
$\int_V (\delta B_{ij}^T A_{ij} ) dV = \int_S (\delta c_i^T T_i) dS $
Where $A_{ij}$ is a second order symmetric tensor. Is this due to the fact that $A=B \to A^T=B^T$ since $A_{ij}$ is symmetric (i.e. $A_{ij}=A_{ji}$)? But what about $T_i$? Shouldn't be $T_i^t$?
Thank you very much for your help
I considered making a comment first, but i think there is only one way to resolve the vague way this question is put forth. I think a good notation here would be-- $$A_{ij}=(A^T)_{ji}$$ I do not think that It doesn't make sense to use the same notation for first-order tensors like $T_i$ and $c_i$, because their transpose changes them from a column vector to a row vector and vice versa.
If answer not satisfactory
Perhaps quoting the book you got this from, or citing it would make the context clearer.