Journal or Book Title
Electronic Journal of Linear Algebra
A new class of sign patterns contained in the class of sign patterns that allow eventual nonnegativity is introduced and studied. A sign pattern is potentially strongly eventually nonnegative (PSEN) if there is a matrix with this sign pattern that is eventually nonnegative and has some power that is both nonnegative and irreducible. Using Perron-Frobenius theory and a matrix perturbation result, it is proved that a PSEN sign pattern is either potentially eventually positive or r-cyclic. The minimum number of positive entries in an n x n PSEN sign pattern is shown to be n, and PSEN sign patterns of orders 2 and 3 are characterized.
Catral, M.; Erickson, C.; Hogben, Leslie; Olesky, D. D.; and van den Driessche, P., "Sign patterns that allow strong eventual nonnegativity" (2012). Mathematics Publications. 250.