Matrices, working definitions

With $n$ unknowns the theory of systems changes little, but the notation becomes cumbersome: it is convenient to gather all the coefficients into an ordered table, the matrix.

An $m\times n$ matrix is a table of numbers with $m$ rows and $n$ columns. We denote it with a capital letter and call $a_{ij}$ the element of row $i$ and column $j$:

$A = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn}\end{pmatrix}.$

If $m=n$ the matrix is said to be square. The matrix $I_n$ with $1$ on the diagonal and $0$ elsewhere is called the identity.

Connections

Topics: Linear systems
Concepts: Matrix · Identity matrix · Square matrix