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Mathematica > Core Language > List Manipulation > Rearranging & Restructuring Lists > Transpose >

Transpose

Transpose[list]
transposes the first two levels in list.

transposes list so that the k

level in list is the

level in the result.

So long as the lengths of the lists at particular levels are the same, the specifications do not necessarily have to be distinct.

Transpose a 2×3 matrix:

Out[1]=

s is a sparse matrix:

Transpose[s] is sparse:

The indices have, in effect, just been reversed:

Enter using Esc tr Esc:

Get the leading diagonal by transposing two identical levels:

Multidimensionalize (in the tensor product sense) a one-dimensional list command:

Accumulate values of a tensor at all levels:

Import data from an image:

Flip the image by reversing at both levels:

T is a tensor with dimensions 2, 3, 4:

Transposing by a permutation

transposes the element positions by

is equivalent to Diagonal[m]:

Transpose only works for rectangular arrays:

Generalize transposition by padding:

Eliminate the padding: