Summary: 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.

15B48, 15B35, 05C50, 15A18

power-positive matrix, eventually positive matrix, requires power-positivity, potentially power-positive, potentially eventually positive, sign pattern