note:The tensors in the new coordinates system are represented by X'.(adsbygoogle = window.adsbygoogle || []).push({});

I have a question about the coordinate transformation of tensor.

σ_{mn}=a_{mi}a_{nj}σ'_{ij}; (1)

ω_{pq}=a_{pk}a_{ql}ω'_{kl}; (2)

In the original coordinates system, we have

σ_{mn}= D_{mpnq}ω_{pq}, (3)

Substituting Eqs.(1) and (2) into Eq.(3), one obtains,

a_{mi}a_{nj}σ'_{ij}=D_{mpnq}a_{pk}a_{ql}ω'_{kl}(4)

then,

σ'_{ij}=a_{mi}a_{nj}a_{pk}a_{ql}D_{mpnq}ω'_{kl}(5)

Here is the problem. How was the Eq.(5) obtained from the Eq.(4). I can't really understand, because the items a_{mi}a_{nj}a_{pk}a_{ql}have changed their position, but their subscript don't change.

Is there any books talking about that?

thanks.

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# About coordinate transformation of tensor.

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