Transpose Matrix

Definition

If $A$ is any $m\times n$ matrix, then the transpose of $A$, denoted by $A^T$, is defined to be the $n\times m$ matrix that results by interchanging the rows and columns of $A$.

That is, the first column of $A^T$ is the first row of $A$, the second column of $A^T$ is the second row of $A$, and so forth.