\begin{definition}[Definition:Matrix/Indices]
Let $\mathbf A$ be an $m \times n$ matrix.
Let $a_{i j}$ be the element in row $i$ and column $j$ of $\mathbf A$.
Then the subscripts $i$ and $j$ are referred to as the '''indices''' (singular: '''index''') of $a_{i j}$.
\end{definition}