Sign patterns that require or allow power-positivity
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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.
This article is published as Catral, Minerva, Leslie Hogben, Dale D. Olesky, and Pauline van den Driessche. "Sign patterns that require or allow power-positivity." The Electronic Journal of Linear Algebra 19 (2010): 121-128. DOI: 10.13001/1081-3810.1352. Posted with permission.