1(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the transpose of a tensor is a tensor.

2. Relevant equations

Definition of the transpose: a[itex]\bullet[/itex]Tb = b[itex]\bullet[/itex]T^Ta where a and be are arbitrary vectors

3. The attempt at a solution

This isn't homework per se, I'm 60 yo and studing continuum mechanics, but I see that I can't use any properties of transposes since I haven't proven first that T^T is a tensor. Likewise I can't use properties of tensors either except for the linear property defintion of a tensor : T(αa + βb) = αTa + βTb

This definition doesn't seem to get me anywhere.

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# Proof that the transpose of a tensor is a tensor

Can you offer guidance or do you also need help?

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