Matrix

Let A be a set of numbers and (m, n) be an ordered pair of positive integers. The coefficient matrix in A, of dimension m × n, that is, of m rows and n columns, is a family ($a_{i,\space j}$) of elements in A indexed by the Cartesian product of the sets of integers [1, m] and [1, n].

$\begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} & … & a_{1,n}\\a_{2,1} & a_{2,2} & a_{2,3} & … & a_{2,n}\\a_{3,1} & a_{3,2} & a_{3,3} & … & a_{3,n}\\ … & … & … & … & …\\a_{m,1} & a_{m,2} & a_{m,3} & … & a_{m,n}\end{pmatrix}$

• In the matrix above, the element $a_{1, 2}$ is read as “$a$ one-two”.
• The first element of the ordered pair in the index indicates the row, whereas the second element indicates the column.
• The element $a_{3, 2}$ is located in the third row and in the second column.