caa a22 4500 463203089 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s00200-007-0042-0 doi (NATIONALLICENCE)springer-10.1007/s00200-007-0042-0 A note on some properties of the Perron root of nonnegative irreducible matrices [Elektronische Daten] [Holger Boche, Sławomir Stańczak] This paper deals with the Perron root of nonnegative irreducible matrices, all of whose entries are continuous bijective functions of some parameter vector. It is known that if the functions are log-convex, then the Perron root is a convex function of the parameter vector. In this paper, we strengthen this result by showing that the log-convexity property is also necessary when the Perron root is required to be convex for any nonnegative irreducible matrix. Furthermore, we show that a less restrictive requirement is sufficient when the matrix is confined to belong to two subsets of irreducible matrices. In particular, in case of positive semidefinite matrices, convexity is sufficient for the Perron root to be convex. Springer-Verlag, 2007 Perron-Frobenius theory nationallicence Log-convexity nationallicence Perron root nationallicence Boche Holger Fraunhofer German-Sino Lab for Mobile Communications, Einsteinufer 37, 10587, Berlin, Germany aut Stańczak Sławomir Fraunhofer German-Sino Lab for Mobile Communications, Einsteinufer 37, 10587, Berlin, Germany aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/4(2007-08-01), 369-378 0938-1279 18:4<369 2007 18 200 https://doi.org/10.1007/s00200-007-0042-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-007-0042-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boche Holger Fraunhofer German-Sino Lab for Mobile Communications, Einsteinufer 37, 10587, Berlin, Germany aut NATIONALLICENCE 700 1- Stańczak Sławomir Fraunhofer German-Sino Lab for Mobile Communications, Einsteinufer 37, 10587, Berlin, Germany aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/4(2007-08-01), 369-378 0938-1279 18:4<369 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer