Overview
The transpose of a matrix converts rows to columns and vice versa. That is, the first row becomes the first column of the transposed matrix, the second row becomes the second column etc....
The following shows the result of the transpose operation on a sample matrix.
{%
\begin{bmatrix}
a & b & c \\
d & e & f\\
g & h & i \\
\end{bmatrix} ^T =
\begin{bmatrix}
a & d & g \\
b & e & h\\
c & f & i \\
\end{bmatrix}
%}