I just found the Samuelson's rule of simplifying the computation of a characteristic polynomial.
$f(\lambda)=\lambda^n-a_1 \lambda^{n-1}+ ...+(-1)^na_n$
$a_1 = Tr(A)$
$a_n = det(A)$
$a_i$ = the sum of the i-rowed diagonal minors of the matrix A
However, I'm unsure how I extend this to a 4x4 matrix.
- Does the sum of the diagonal minors need to be in front of the $\lambda^2$ term? In that case, which coefficient does come in form of the $\lambda$ term?
Thanks a lot in advance,