What a matrix is
Matrix
A matrix is a mathematical object that arranges numbers in rows and columns. The numbers can come from any of the familiar sets: $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$ or $\mathbb{R}$.
Order
The order of a matrix is its number of rows and columns. We write $A_{n\times m}$ for the matrix $A$ with $n$ rows and $m$ columns: rows first, then columns.
Example
$$A_{2\times 3} = \begin{pmatrix} 5 & 1 & 4 \\ 2 & 3 & 1 \end{pmatrix}$$
A matrix is a way of storing data in order. In class the rows were labelled A and B and the columns M, F and SoS:
| M | F | SoS | |
|---|---|---|---|
| A | 5 | 1 | 4 |
| B | 2 | 3 | 1 |
The entries
$a_{i,j}$ (or $a_{ij}$) is the entry in row $i$ and column $j$. In the example, $a_{1,2} = 1$ and $a_{2,3} = 1$. A matrix is sometimes written in short as $A = (a_{ij})$.