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Proof that the transpose of a tensor is a tensor

  • Thread starter wonfish
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Homework Statement


Prove that the transpose of a tensor is a tensor.



Homework Equations


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



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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