Lets say we have a Complex Matrix
$$ \begin{matrix} a+ib & c+id \\ e+if & g+ih & \end{matrix} $$
MATLAB shows the transpose of this matrix as
$$ \begin{matrix} a-ib & e-if \\ c-id & g-ih & \end{matrix} $$
But why do we do this? Why isn't it simply
$$ \begin{matrix} a+ib & e+if \\ c+id & g+ih & \end{matrix} $$
There is Conjugate Transpose of a Matrix. What about Simple Transpose? Why doesn't it exist?
You have the two MATLAB commands
$(i)$ B=A.' Gives simple transposed matrix (without complex conjugate)
$(ii)$ B=A' Gives conjugate transpose