Matrix
A matrix (pl.: matrices) is a rectangular array of values arranged in rows and columns. Matrices are often used to represent mathematical objects or the properties of such objects.
The shape of a matrix is often communicated through the number of rows and columns, e.g. $m\times n$ matrix where $m$ is the number of rows and $n$ is the number of columns.
Consider the following matrix: $\displaystyle \begin{bmatrix}a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \end{bmatrix}$
This would be commonly referred to as a “$2\times 3$ matrix”, or a “two by three matrix”. Rows always come before columns.