  This paper studies commuting matrices in max algebra and nonnegative linear
algebra. Our starting point is the existence of a common eigenvector, which
directly leads to max analogues of some classical results for complex matrices.
We also investigate Frobenius normal forms of commuting matrices, particularly
when the Perron roots of the components are distinct. For the case of max
algebra, we show how the intersection of eigencones of commuting matrices can
be described, and we consider connections with Boolean algebra which enables us
to prove that two commuting irreducible matrices in max algebra have a common
eigennode.
