Transpose

The transpose of $A$, written $A^{T}$, reflects it across its diagonal: the entry at row $i$, column $j$ moves to row $j$, column $i$. A $200 \times 50$ matrix becomes $50 \times 200$.

It shows up constantly because it is how you make shapes line up for multiplication — $A^{T}B$ is legal when $AB$ is not. It is also the reason the backward pass of a linear layer multiplies by the weight matrix transposed rather than the weight matrix itself.

Worth distinguishing from reshape. Transposing moves data so that the values follow their new positions; reshaping keeps the memory order and re-cuts it into a new shape. Both change the shape and only one preserves meaning, so using reshape to reorder axes silently scrambles the contents.