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## Main Question or Discussion Point

I just started reading Landau and Lifschitz'

The explanation given was that the four-tensor is a 4x4 matrix A

Am I correct in my understanding that this means that element a

So if I have, for instance, a'

*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 A

_{ik}with the property that for some transformation α_{ik}, elements of A_{ik}are related to elements of the tensor A'_{ml}in the transformed coordinates by the equation A_{ik}= α_{im}α_{kl}A'_{ml}.Am I correct in my understanding that this means that element a

_{ik}of A_{ik}is related to element a'_{ml}of A_{ml}, for some i, k, m, l, by the product α_{im}α_{kl}?So if I have, for instance, a'

_{23}and I want to find a_{14}, then i = 1, k = 4, m = 2, and l = 3, so I multiply a'_{23}by the product of the elements α_{12}and α_{43}of the transformation matrix α? Or am I misunderstanding that?