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Earlier sources may be seen to use the words constituent or even coordinate, but these names have now been superseded.