The transpose Aᵀ swaps rows and columns: element at row i, column j moves to row j, column i. An m×n matrix becomes n×m after transpose.

Used constantly in ML: dot product via matrix multiply (aᵀb = a dot b), computing covariance matrices (XᵀX), backpropagation weight gradient computation (δW = xᵀδ), and the attention formula Q Kᵀ / √dₖ in transformers. A symmetric matrix equals its own transpose (A = Aᵀ) - the covariance matrix is always symmetric. Understanding transpose is prerequisite for reading neural network math notation.