TITLE: Perron-Frobenius theory for reducible matrices
QUESTION [12 upvotes]: Can someone suggest some sources/references dealing with the Perron-Frobenius theory for nonnegative matrices that are reducible?
Specifically, if $A\ge 0$ is a $d\times d$ matrix with no assumptions about irreducibility, I am interested the precise description of
a) the set of all non-negative eigenvectors $v\ge 0$ in $R^d$ for $A$;
and
b) the dynamics of the action of $A$ on the non-negative quadrant $W=\{w\in R^d | w\ge 0\}$, particularly the limiting behavior (up to projectivization) of the sequences $A^nw$ where $w\in W$ and $n=1,2,3,...$.
The standard sources on the Perron-Frobenius theory only deal with primitive and irreducible nonnegative matrices, and I could not find any sources that treat in detail the case of an arbitrary $d\times d$ matrix $A\ge 0$.

REPLY [2 votes]: I recently ran into a similar problem.  Something that helped me a lot was Chapter 9 of the first edition of the Handbook of Linear Algebra (which seems to be Chapter 10 of the second edition---just look for something written by Rothblum), edited by Professor Hogben.