# Dictionary:Transpose

The transpose AT of a matrix A is the matrix whose rows are identical to the columns of A. Thus if matrix A is of size ${\displaystyle (m\times n)}$, matrix AT is of size ${\displaystyle (n\times m)}$. For conformable matrices,
${\displaystyle (AB)^{T}=B^{T}A^{T}}$.
${\displaystyle (A^{T})^{T}=A}$.