I just started reading Landau and Lifschitz' Classical Theory of Fields today and I reached the section on the spacetime four-tensor. The explanation given was that the four-tensor is a 4x4 matrix Aik with the property that for some transformation αik, elements of Aik are related to elements of the tensor A'ml in the transformed coordinates by the equation Aik = αimαklA'ml. Am I correct in my understanding that this means that element aik of Aik is related to element a'ml of Aml, for some i, k, m, l, by the product αimαkl? So if I have, for instance, a'23 and I want to find a14, then i = 1, k = 4, m = 2, and l = 3, so I multiply a'23 by the product of the elements α12 and α43 of the transformation matrix α? Or am I misunderstanding that?