Thanks for your help but i still don't really understand how to find a formula for (I-B)^-1 in terms of powers of B. What do you mean by the series is a finite sum because of the nilpotency??
Thanks for your help but i still don't really understand how to find a formula for (I-B)^-1 in terms of powers of B. What do you mean by the series is a finite sum because of the nilpotency??
If B is nilpotent then B^N=0 for some positive integer N. Thus the series finishes with the term B^{N–1}, since all the subsequent terms are zero. That suggests that , a conjecture which you can verify by checking that .