matrix A
satisfies the polynomial equation 
, where 
is the
characteristic polynomial of degree d.
This implies that 
, where
. If A has n distinct
eigenvalues 
, the coefficients 
can be found by solving the system of
equations 
.
A quick method that finds a characteristic polynomial due to K... is to solve the
system of linear equations for the coefficients: pick a vector 
at random and
solve
for 
the equations
. If the resulting matrix is singular,
re-sample until a non-singular matrix is found.