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Transpose
Transpose[
list
] transposes the first two levels in list.
Transpose[
list
,
,
, ... 
] transposes list so that the k
 level in list is the 
 level in the result.
Example: Transpose[
a,b
,
c,d
] .
Transpose gives the usual transpose of a matrix.
Acting on a tensor 
Transpose gives the tensor  .
Transpose[
list
,
,
, ... 
] gives the tensor  .
So long as the lengths of the lists at particular levels are the same, the specifications  do not necessarily have to be distinct.
Example: Transpose[Array[a,
3, 3
],
1, 1
].
See the Mathematica book: Section 1.8.3, Section 1.8.12, Section 3.7.2, Section 3.7.7.
See also: Flatten.
Related package: LinearAlgebra`MatrixManipulation`.
Further Examples
This is the transpose of a non-square matrix.
In[1]:= 
Out[1]//MatrixForm= 
Here is a tensor, its transpose, and their dimensions.
In[2]:= 
Out[2]//MatrixForm= 
In[3]:= 
Out[3]//MatrixForm= 
Here is a tensor, its transpose, and their dimensions.
In[4]:= 
Out[4]= 
In[5]:= 
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