Geodesic
Sign patterns that require or allow power-positivity
The electronic journal of linear algebra, Tome 19 (2009), pp. 121-128.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 15B48, 15B35, 05C50, 15A18
Keywords: power-positive matrix, eventually positive matrix, requires power-positivity, potentially power-positive, potentially eventually positive, sign pattern 
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     author = {Catral, Minerva and Hogben, Leslie and Olesky, Dale D. and van den Driessche, Pauline},
     title = {Sign patterns that require or allow power-positivity},
     journal = {The electronic journal of linear algebra},
     pages = {121--128},
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     volume = {19},
     year = {2009},
     language = {en},
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Catral, Minerva; Hogben, Leslie; Olesky, Dale D.; van den Driessche, Pauline. Sign patterns that require or allow power-positivity. The electronic journal of linear algebra, Tome 19 (2009), pp. 121-128. http://geodesic.mathdoc.fr/item/ELA_2009__19__a0/