Geodesic
Sign patterns that allow eventual positivity
The electronic journal of linear algebra, Tome 19 (2009), pp. 108-120.

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

Summary: Several necessary or sufficient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n $\geq 2$, the minimum number of positive entries in an n $\times n$ sign pattern that allows eventual positivity is n + 1, and to classify all $2 \times 2$ and $3 \times 3$ sign patterns as to whether or not the pattern allows eventual positivity. A $3 \times 3$ matrix is presented to demonstrate that the positive part of an eventually positive matrix need not be primitive, answering negatively a question of Johnson and Tarazaga.
Classification : 15B48, 15B35, 05C50, 15A18
Keywords: eventually positive matrix, potentially eventually positive sign pattern, Perron- Frobenius, directed graph 
@article{ELA_2009__19__a1,
     author = {Berman, Abraham and Catral, Minerva and Dealba, Luz Maria and Elhashash, Abed and Hall, Frank J. and Hogben, Leslie and Kim, In-Jae and Olesky, Dale D. and Tarazaga, Pablo and Tsatsomeros, Michael J. and van den Driessche, Pauline},
     title = {Sign patterns that allow eventual positivity},
     journal = {The electronic journal of linear algebra},
     pages = {108--120},
     publisher = {mathdoc},
     volume = {19},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2009__19__a1/}
}
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%A Kim, In-Jae
%A Olesky, Dale D.
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%A van den Driessche, Pauline
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Berman, Abraham; Catral, Minerva; Dealba, Luz Maria; Elhashash, Abed; Hall, Frank J.; Hogben, Leslie; Kim, In-Jae; Olesky, Dale D.; Tarazaga, Pablo; Tsatsomeros, Michael J.; van den Driessche, Pauline. Sign patterns that allow eventual positivity. The electronic journal of linear algebra, Tome 19 (2009), pp. 108-120. http://geodesic.mathdoc.fr/item/ELA_2009__19__a1/