B&F have the following:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\delta_{i j} = e'_i \cdot e'_j = a_{i k} \left( e_k \cdot e'_j \right) = a_{i k} a_{j k} [/itex]

and they ask the reader to show that

[itex] a_{k i} a_{k j} = \delta_{i j} [/itex]

Does it suffice to show the following? :

[itex] \delta_{i j} = a_{i k} a_{j k} \to \delta_{j i} = \left( a_{i k} a_{j k} \right)^T = a_{k i} a_{k j} [/itex]

and note that

[itex] \delta_{j i} = \delta_{i j} [/itex]

?

I believe this is sufficient, but I have a feeling I short-cut this.

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# Taking vectors from one basis to another [Byron and Fuller]

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