Definition:Array/Element

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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 $a_{i j}$.

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.