How do you transpose tensors? We transpose a matrix $A$ by replacing $A_{ij}$ with $A_{ji}$, for all $i$ and $j$.
However, in case $A$ has more than two dimensions (that is, it is a tensor), I don't know how to apply the transpose operation.


*

*If A has dimensions $3\times 3 \times 8$, then what will replace $A_{ijk}$? 

*If $A$ has shape $3\times 3\times 8\times 8$, then what will replace $A_{ijkl}$?

The operation of taking a transpose is closely related to the concept of symmetry.  One paper that addresses this is http://www.iaeng.org/publication/WCE2010/WCE2010_pp1838-1841.pdf. I have been researching $2^m$ dimensional matrices where the indices are zeros and ones.  The transpose is found by changing all zeros to ones and ones to zeros.   
