$$ boldsymbolA=beginbmatrix a_11 & a_12 & a_13 & a_14 a_21 & a_22 & a_23 & a_

24}\ a_{31} & a_{32} & a_{33} & a_{34}\ a_{41} & a_{42} & a_{43} & a_{44} \end{bmatrix} $$

The transpose of matrix $\boldsymbol{A}$ is denoted as $\boldsymbol{A}^T$ and is obtained by interchanging the rows and columns of $\boldsymbol{A}$. That is,

$$ \boldsymbol{A}^T=\begin{bmatrix} a_{11} & a_{21} & a_{31} & a_{41}\ a_{12} & a_{22} & a_{32} & a_{42}\ a_{13} & a_{23} & a_{33} & a_{43}\ a_{14} & a_{24} & a_{34} & a_{44} \end{bmatrix} $$

For example, if

$$ \boldsymbol{A}=\begin{bmatrix} 1 & 2 & 3\ 4 & 5 & 6 \end{bmatrix} $$

then

$$ \boldsymbol{A}^T=\begin{bmatrix} 1 & 4\ 2 & 5\ 3 & 6 \end{bmatrix} $$

Note that the dimensions of $\boldsymbol{A}$ and $\boldsymbol{A}^T$ are reversed. That is, if $\boldsymbol{A}$ is an $m\times n$ matrix, then $\boldsymbol{A}^T$ is an $n\times m$ matrix