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 Documentation / Mathematica / Built-in Functions / Lists and Matrices / Matrix Operations  /
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 3.7.2Section 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]:=