Matrix : A $m\times n$ matrix is a rectangular arrangement of $m\cdot n$ numbers into $m$ rows and $n$ columns. For example $\begin{pmatrix}1&2&3\\4&5&6\\\end{pmatrix}$ is a $3\times 2$ matrix. $A_{ij}$ refers to the element of $A$ in the i-th row and j-th column.