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
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}} Transpose Mathematica
Transpose[m, {1, 1}] on a square matrix returns the main diagonal, equivalent to Diagonal[m] . 4. Important Constraints Transpose[{{a, b, c}, {d, e, f}}] Output: {{a,
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 arrays with depth greater than 2, Transpose