Definition:Matrix/Element

Definition
Let $\mathbf A$ be an $m \times n$ matrix over a set $S$.

The individual $m \times n$ elements of $S$ that go to form $\mathbf A = \sqbrk a_{m n}$ are known as the elements of the matrix.

The element at row $i$ and column $j$ is called element $\tuple {i, j}$ of $\mathbf A$, and can be written $a_{i j}$, or $a_{i, j}$ if $i$ and $j$ are of more than one character.

If the indices are still more complicated coefficients and further clarity is required, then the form $a \tuple {i, j}$ can be used.

Note that the first subscript determines the row, and the second the column, of the matrix where the element is positioned.

Also denoted as
Some sources prefer to use the uppercase form of the letter for the matrix element:
 * $A_{i j}$

Also known as
An element of a matrix is sometimes seen as entry of a matrix, or just (matrix) entry.

Earlier sources may be seen to use the words constituent or even coordinate, but these names have now been superseded.