Introduction to Matrices

A matrix is an array of numbers. In $$\LaTeX$$ we represent it like this:

The characteristic polynomial $\chi(\lambda)$ of the

$3 \times 3$ matrix \[ \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right)\]  is given by the formula \[ \chi(\lambda) = \left| \begin{array}{ccc} \lambda - a & -b & -c \\ -d & \lambda - e & -f \\ -g & -h & \lambda - i \end{array} \right|.\] 

Neat; eh?