Geodesic
The generalized monotonicity property of the Perron root
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 13-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property implies known monotonicity properties and also the Chistyakov two-sided bounds for the Peroon root of a block-partitioned nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov's theorem are analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. 
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Yu. A. Alpin; L. Yu. Kolotilina. The generalized monotonicity property of the Perron root. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 13-29. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a1/

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