1. The problem statement, all variables and given/known data A function of a hermitian operator H can be written as f(H)=Σ (H)n with n=0 to n=∞. When is (1-H)-1 defined? 2. Relevant equations (1-x)-1 = Σ(-x)n= 1-x+x2-x3+... 3. The attempt at a solution (1-H)-1 converges if each element of H converges in this series, that is (1-hi)-1 converges with hi being the diagonal elements of the hermitian operator H. So Σ(-hi)n should converge. By the ratio test, (-hi)n+1/(-hi)n = |hi|. So it converges if |hi|<1. Is this correct?