The transpose of a matrix is simply the swapping of the rows and columns of a matrix. $\mathbf{B} = \mathbf{A}^T$ $b_{ij}=a_{ji}$ >[!example]- $\begin{bmatrix}1&2\\3&4\\5&6\end{bmatrix}^T=\begin{bmatrix}1&3&5\\2&4&6\end{bmatrix}$