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

Transpose

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

Transpose[list, {n₁, n₂, ...}]
transposes list so that the k

level in list is the n_k

level in the result.

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

Transpose a 2×3 matrix:

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

^-1:

Transpose[m, {1, 1}] is equivalent to Diagonal[m]:

Transpose only works for rectangular arrays:

Generalize transposition by padding:

Eliminate the padding: