Geodesic
Matrix functions preserving sets of generalized nonnegative matrices
The electronic journal of linear algebra, Tome 20 (2010), pp. 673-690.

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

Summary: Matrix functions preserving several sets of generalized nonnegative matrices are characterized. These sets include PFn, the set of n $\times n$ real eventually positive matrices; and WPFn, the set of matrices A $\in R$ n $\times n$ such that A and its transpose have the Perron-Frobenius property. Necessary conditions and sufficient conditions for a matrix function to preserve the set of n $\times n$ real eventually nonnegative matrices and the set of n $\times n$ real exponentially nonnegative matrices are also presented. In particular, it is shown that if f (0) = 0 and f $^{\prime}$ (0) = 0 for some entire function f , then such an entire function does not preserve the set of n $\times n$ real eventually nonnegative matrices. It is also shown that the only complex polynomials that preserve the set of n $\times n$ real exponentially nonnegative matrices are $p(z) = az + b$, where a, b $\in R$ and a $\geq 0$.
Classification : 15A48
Keywords: matrix functions, generalization of nonnegative matrices, eventually nonnegative matrices, eventually positive matrices, exponentially nonnegative matrices, eventually exponentially nonnegative matrices, Perron-Frobenius property, strong Perron-Frobenius property 
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     author = {Elhashash, Abed and Szyld, Daniel B.},
     title = {Matrix functions preserving sets of generalized nonnegative matrices},
     journal = {The electronic journal of linear algebra},
     pages = {673--690},
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     volume = {20},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2010__20__a6/}
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Elhashash, Abed; Szyld, Daniel B. Matrix functions preserving sets of generalized nonnegative matrices. The electronic journal of linear algebra, Tome 20 (2010), pp. 673-690. http://geodesic.mathdoc.fr/item/ELA_2010__20__a6/