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 the matrix $\mathbf A = \left[{a}\right]_{m n}$ are known as the elements of the matrix.

That is, an element of a matrix is an element of the image of that matrix.

The element at row $i$ and column $j$ is called element $\left({i, j}\right)$ of the matrix, and can be written $a_{i j}$, or $a_{i, j}$ if $i$ and $j$ are more complicated coefficients and more clarity is needed.

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

Also known as
The elements of a matrix are sometimes seen as entries of a matrix.