note:The tensors in the new coordinates system are represented by X'. I have a question about the coordinate transformation of tensor. σmn=amianjσ'ij; (1) ωpq=apkaqlω'kl; (2) In the original coordinates system, we have σmn = Dmpnqωpq, (3) Substituting Eqs.(1) and (2) into Eq.(3), one obtains, amianjσ'ij=Dmpnqapkaqlω'kl (4) then, σ'ij=amianjapkaqlDmpnqω'kl (5) Here is the problem. How was the Eq.(5) obtained from the Eq.(4). I can't really understand, because the items amianjapkaql have changed their position, but their subscript don't change. Is there any books talking about that? thanks.