Geodesic
On general matrices having the Perron-Frobenius property
The electronic journal of linear algebra, Tome 17 (2008), pp. 389-413.

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

Summary: A matrix is said to have the Perron-Frobenius property if its spectral radius is an eigenvalue with a corresponding nonnegative eigenvector. Matrices having this and similar properties are studied in this paper as generalizations of nonnegative matrices. Sets consisting of such generalized nonnegative matrices are studied and certain topological aspects such as connectedness and closure are proved. Similarity transformations leaving such sets invariant are completely described, and it is shown that a nonnilpotent matrix eventually capturing the Perron-Frobenius property is in fact a matrix that already has it.
Classification : 15A48
Keywords: perron-Frobenius property, generalization of nonnegative matrices, eventually nonnegative matrices, eventually positive matrices 
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     title = {On general matrices having the {Perron-Frobenius} property},
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Elhashash, Abed; Szyld, Daniel B. On general matrices having the Perron-Frobenius property. The electronic journal of linear algebra, Tome 17 (2008), pp. 389-413. http://geodesic.mathdoc.fr/item/ELA_2008__17__a17/