Hadamard functions preserving nonnegative H-matrices Elsner, Ludwig Hershkowitz, Daniel Hadamard matrix functions H-matrices spectral radius of nonnegative matrices For k nonnegative n x n matrices A(l) = (a(ij)(l)) and a function f : R<INF>+</INF><SUP>k</SUP> --> R<INF>+ </INF>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. ELSEVIER SCIENCE INC 1998 info:eu-repo/semantics/article doc-type:article text https://pub.uni-bielefeld.de/record/1625037 Elsner L, Hershkowitz D. Hadamard functions preserving nonnegative H-matrices. <em>Linear Algebra and its Applications</em>. 1998;279(1-3):13-19. eng info:eu-repo/semantics/altIdentifier/doi/10.1016/S0024-3795(97)10094-5 info:eu-repo/semantics/altIdentifier/issn/0024-3795 info:eu-repo/semantics/altIdentifier/wos/000075426400002 info:eu-repo/semantics/closedAccess