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I wasn't sure whether to post this here on in some of the physics sections.

I have a rank 2 tensor in one coordinate reference system [x1, x2, x3], the one where only the principal elements are non zero: R=[ a11 0 0; 0 a22 0; 0 0 a33 ].

I want the tensor R in some other orthogonal coordinate reference system. I have the transformation matrix U from the system [x1, x2, x3] to the second one [X1, X2, X3].

I know how to use U to transform vectors from one system to the other:

[V1; V2; V3]= U [v1; v2; v3]

But I don't know what operation to do to transform a tensor. I'm led to believe that it could be something like

[R(in Xi)] = U^-1 R(in xi) U

But I'm not sure whether this is right nor what's the rationale for it.

I would appreciate any help you could give me.

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# Transformation matrix on tensors

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