Max algebra, Ultimate periodicity, Perron-Frobenius, Eigenspace, Core.
The max-algebraic core of a nonnegative matrix is the intersection of column spans of all max-algebraic matrix powers. This paper investigates the action of a matrix on its core. Being closely related to ultimate periodicity of matrix powers, this study leads to new modifications and geometric characterizations of robust, orbit periodic and weakly stable matrices
Butkovic, Peter; Schneider, Hans; and Sergeev, Sergei.
"On the max-algebraic core of a nonnegative matrix",
Electronic Journal of Linear Algebra,