Geodesic
Sign patterns that require a positive or nonnegative left inverse
The electronic journal of linear algebra, Tome 17 (2008), pp. 209-218.

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

Summary: An m by n sign pattern A is an m by n matrix with entries in +, - , 0. The sign pattern A requires a positive (resp. nonnegative) left inverse provided each real matrix with sign pattern A has a left inverse with all entries positive (resp. nonnegative). In this paper, necessary and sufficient conditions are given for a sign pattern to require a positive or nonnegative left inverse. It is also shown that for n $\geq 2$, there are no square sign patterns of order n that require a positive (left) inverse, and that an n by n sign pattern requiring a nonnegative (left) inverse is permutationally equivalent to an upper triangular sign pattern with positive main diagonal entries and nonpositive off-diagonal entries.
Classification : 15A06, 15A09, 15A48, 05C20
Keywords: nonnegative left inverse, positive left inverse, sign-consistent constrained system, sign pattern 
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     title = {Sign patterns that require a positive or nonnegative left inverse},
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     year = {2008},
     language = {en},
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Kim, In-Jae; Shader, Bryan L. Sign patterns that require a positive or nonnegative left inverse. The electronic journal of linear algebra, Tome 17 (2008), pp. 209-218. http://geodesic.mathdoc.fr/item/ELA_2008__17__a29/