The Companion Matrix

Suppose we have a nonconstant polynomial
$p( \lambda )=a_0 + a_1 \lambda + a_2 \lambda^2 +...+ a_n \lambda^n$
.
The companion matrix associated with this polynomial is the square matrix with the diagonal below the leading diagonal consisting only of 1's, last column of the negative coefficients of
$\lambda^i , \: i=0,1,...,n-1$
and all other entries zero.
Example:
$p( \lambda )=-2+3 \lambda +4 \lambda^2- \lambda^3$
.
The companion matrix is
$\left( \begin{array}{ccc} 0 & 0 & 2 \\ 1 & 0 & -3 \\ 0 & 1 & -4 \end{array} \right)$