Matrix Transpose

The transpose of a matrix $A$ is an operation which flips the matrix along its diagonal.

$$\begin{array}{rl}A& =\left(\begin{array}{cccc}a& b& c& d\\ e& f& g& h\end{array}\right)\\ A^T& =\left(\begin{array}{cc}a& e\\ b& f\\ c& g\\ d& h\end{array}\right)\\ {\left(\begin{array}{c}{A}^T\end{array}\right)}^T& =A\end{array}$$