Sign patterns that allow strong eventual nonnegativity
Published in Electron. J. Linear Algebra, 2012
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-by-n PSEN sign pattern is shown to be n, and PSEN sign patterns of orders 2 and 3 are characterized.
Recommended citation: M. Catral, C. Erickson, L. Hogben, D.D. Olesky, and P. Van den Driessche. “Sign patterns that allow strong eventual nonnegativity.” Electron. J. Linear Algebra 23 (2012), 1—10.