Suppose I found out the eigenvalues of the Leslie matrix (may not be the form in Wikipedia) that describe some discrete recurrence relation between e.g. different age classes. Can I conclude anything if the largest eigenvalue $\lambda_{\max} > 1, = 1, \in (0, 1), = 0$ or $< 0$ (this may not happen, but just in case it did)?
When $\lambda_{\max} = 1$, can I say the eigenvector I obtained is the steady-state solution to the equation system $\underline{x_{n+1}} = L\underline{x_n}$?
Thanks in advance.