The transpose $A^T$ exchanges rows and columns: $(A^T)_{ij}=a_{ji}$. If $A$ is $m\times n$, then $A^T$ is $n\times m$. Example: $\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}^T=\begin{bmatrix}1&4\\2&5\\3&6\end{bmatrix}$. Transposition alone does not conjugate complex entries.
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