11. 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.