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}}
In the Wolfram Language (Mathematica), the Transpose function is a fundamental tool for restructuring data, ranging from basic 2D matrices to complex multidimensional tensors. 1. Basic Matrix Transposition
Transpose only works on "rectangular" arrays, meaning all sub-lists at a given level must have the same length. Transpose Mathematica
Transposition is used to rotate images 90°. A 90° clockwise rotation involves finding the transpose and then reversing each row.
You can use the superscript postfix operator m by typing ESC tr ESC . 2. Multi-Level Transposition (Tensors) For a standard matrix (a list of lists),
When you have several lists of data (e.g., separate
For simple 2D lists, Thread[list] is often used as a more readable shorthand for transposing the first two levels. You can use the superscript postfix operator m
Transpose[m, {1, 1}] on a square matrix returns the main diagonal, equivalent to Diagonal[m] . 4. Important Constraints