Transpose Mathematica (2025)

For simple 2D lists, Thread[list] is often used as a more readable shorthand for transposing the first two levels.

Transpose[m, {1, 1}] on a square matrix returns the main diagonal, equivalent to Diagonal[m] . 4. Important Constraints

Transposition is used to rotate images 90°. A 90° clockwise rotation involves finding the transpose and then reversing each row. Transpose Mathematica

For a standard matrix (a list of lists), Transpose[m] interchanges its rows and columns. Transpose[{{a, b, c}, {d, e, f}}] Output: {{a, d}, {b, e}, {c, f}}

Mathematica treats matrices as nested lists. For arrays with depth greater than 2, Transpose can take a second argument to specify how levels (dimensions) should be rearranged. Transpose[list] Transposes the first two levels by default. Transpose[list, {n1, n2, ...}] Rearranges the list so the -th level becomes the -th level in the result. Transpose[list, m <-> n] Swaps specifically levels , leaving others unchanged. Transpose[list, k] Cycles all levels positions to the right. 3. Key Use Cases For simple 2D lists, Thread[list] is often used

Transpose only works on "rectangular" arrays, meaning all sub-lists at a given level must have the same length.

You can use the superscript postfix operator m by typing ESC tr ESC . 2. Multi-Level Transposition (Tensors) Important Constraints Transposition is used to rotate images

For formal tensor algebra, TensorTranspose provides similar functionality but is optimized for use with symbolic tensors and operations like TensorContract .