# Definition:Array/Element

## Definition

Let $\mathbf A$ be an Array.

The individual $n \times n$ symbols that go to form $\mathbf L$ are known as the **elements** of $\mathbf L$.

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 $a \left({i, j}\right)$ can be used.

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

### Index of Element

Let $\mathbf A$ be an $m \times n$ array.

Let $a_{i j}$ be an element of $\mathbf A$.

Then the subscripts $i$ and $j$ are referred to as the **indices** (singular: **index**) of $a_{i j}$.

### Absolute Address

When referring to a specific element of $\mathbf A$ directly by its indices $\tuple {i, j}$, those indices can be referred to as the **absolute address** of that element.

This terminology is most often seen in the context of computer spreadsheet programs.

## Also denoted as

Some sources prefer to use the uppercase form of the letter for the **element**:

- $ A_{i j}$

## Also known as

The **elements of an array** are sometimes seen as **entries of an array**.