Sign patterns that require or allow power-positivity
Minerva Catral, Leslie Hogben, Dale D. Olesky, Pauline Van den Driessche · Electronic Journal of Linear Algebra · 2009
A matrix A is power-positive if some positive integer power of A is entrywise positive. A sign pattern A is shown to require power-positivity if and only if either A or −A is nonnegative and has a primitive digraph, or equivalently, either A or −A requires eventual positivity. A sign pattern A is shown to be potentially power-positive if and only if A or −A is potentially eventually positive.