Context: I'm reading this paper http://portal.acm.org/citation.cfm?id=1382468

Definitions:

$B_1 = I$

$B_{k+1} = AB_k - \frac{1}{k} tr (AB_k)I$

$det(A) = \frac{(-1)^n}{n} tr(AB_n)$

Question: How does this formula for the determinant work?

I understand: (1) the definition of determinant via permutations

(2) the definition of determinant via minors $det(A) = \sum_i (-1)^{i+j} a_{i,j}det(A_{i,j})$

(3) the Cayley-Hamilton Theorem: $p(s) = det(sI-A)$, $p(A)=0$.

What I fail to understand: how the above recurrence works. If you could tell me the key idea (or give me a term to google for), I can finish the derivation myself.

Thanks!