In the transformation of tensor components when changing the co-ordinate system, can someone explain the following:(adsbygoogle = window.adsbygoogle || []).push({});

Firstly, what is the point in re-writing the indicial form (on the left) as a_{ik}T_{kl}a_{jl}? Since we're representing the components in a matrix, and the transformation matrix is also a matrix, aren't we violating the non-commutativity of matrix multiplication (AB ≠ BA)?

Secondly, how does this meanin matrix form? Why are we transposing the matrix?A T A^{T}

Thanks in advance

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# I Transformation of Tensor Components

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