@article{1625037,
abstract = {For k nonnegative n x n matrices A(l) = (a(ij)(l)) and a function f : R+^{k} --> R+ consider the matrix C = f(A(l),...,A(k)) = (C-ij), where c(ij) = f(a(ij)(l),...,a(ij)(k)), i,j=l,...,n. Denote by rho(A) the spectral radius of a nonnegative square matrix A, and by sigma(A) the minimal real eigenvalue of its comparison matrix M(A) = 2 diag(a(ii)) -A. It is known that the function f(x(1),...,x(k)) = cx(1)(alpha 1)...x(k)(alpha k), where alpha(i) is an element of R+, Sigma(i=l)(k) alpha(i) greater than or equal to 1 and c > 0, satisfies the inequalities rho(f(A(1),...,A(k))) less than or equal to f(rho(A(1)),...,rho(A(k))), as well as the in equalities sigma(f(A(1),...,A(k))) greater than or equal to f(sigma(A(1)),...,sigma(A(k))). whenever A(i) are nonnegative H-matrices, i.e. sigma(A(i)) greater than or equal to 0. The last inequality implies that the above function f` maps the set of nonnegative I-I-matrices into itself. In this note it is proven that these are the only continuous functions with this property. (C) 1998 Elsevier Science Inc. AU rights reserved.},
author = {Elsner, Ludwig and Hershkowitz, Daniel},
issn = {0024-3795},
journal = {Linear Algebra and its Applications},
keyword = {Hadamard matrix functions, H-matrices, spectral radius of nonnegative, matrices},
number = {1-3},
pages = {13--19},
publisher = {ELSEVIER SCIENCE INC},
title = {{Hadamard functions preserving nonnegative H-matrices}},
doi = {10.1016/S0024-3795(97)10094-5},
volume = {279},
year = {1998},
}