- #1
wonfish
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1
Prove that the transpose of a tensor is a tensor.
Definition of the transpose: a[itex]\bullet[/itex]Tb = b[itex]\bullet[/itex]T^Ta where a and be are arbitrary vectors
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.
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.