Dictionary:Transpose

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

$(AB)^{T}=B^{T}A^{T}$.

For any matrix,

$(A^{T})^{T}=A$.