Eventually nonnegative matrix, exponentially nonnegative matrix, Perron-Frobenius, proper cone
Eventually nonnegative matrices are square matrices whose powers become and remain (entrywise) nonnegative. Using classical Perron-Frobenius theory for cone preserving maps, this notion is generalized to matrices whose powers eventually leave a proper cone K ⊂ R^n invariant, that is, A^mK ⊆ K for all sufficiently large m. Also studied are the related notions of eventual cone invariance by the matrix exponential, as well as other generalizations of M-matrix and dynamical system notions.
Kasigwa, Michael and Tsatsomeros, Michael.
"Eventual Cone Invariance",
Electronic Journal of Linear Algebra,
Volume 32, pp. 204-216.