I'm working out of Deuflhard and Bornemann's Scientific Computing with ODEs (Springer 2000).
The statement is:
Moreover, $\tau_c = \tau_c^+$ holds if all eigenvalues $\lambda \in \sigma(A)$ ... have index $\iota(\lambda)=1$.
In my case, I've found that $A$ has two eigenvalues, $\lambda = \{1,1000\}$. Being more of a programmer, I tend to think of the index of the position in the set, i.e. index(1) = 0
, index(1000) = 1
, etc. -- but its pretty clear from the rest of the section that there is some other definition of index that I'm not aware of.
I can do most of the leg work myself learning about it, but googling permutations of "eigenvalue index" haven't been very helpful.
Thanks in advance.