[{"_id":"1625037","citation":{"lncs":" Elsner, L., Hershkowitz, D.: Hadamard functions preserving nonnegative H-matrices. Linear Algebra and its Applications. 279, 13-19 (1998).","apa_indent":"Elsner, L., & Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications*, *279*(1-3), 13-19. doi:10.1016/S0024-3795(97)10094-5

","mla":"Elsner, Ludwig, and Hershkowitz, Daniel. “Hadamard functions preserving nonnegative H-matrices”. *Linear Algebra and its Applications* 279.1-3 (1998): 13-19.","apa":"Elsner, L., & Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications*, *279*(1-3), 13-19. doi:10.1016/S0024-3795(97)10094-5","angewandte-chemie":"L. Elsner, and D. Hershkowitz, “Hadamard functions preserving nonnegative H-matrices”, *Linear Algebra and its Applications*, **1998**, *279*, 13-19.","harvard1":"Elsner, L., & Hershkowitz, D., 1998. Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications*, 279(1-3), p 13-19.","chicago":"Elsner, Ludwig, and Hershkowitz, Daniel. 1998. “Hadamard functions preserving nonnegative H-matrices”. *Linear Algebra and its Applications* 279 (1-3): 13-19.

","default":"Elsner L, Hershkowitz D (1998)

*Linear Algebra and its Applications* 279(1-3): 13-19.","wels":"Elsner, L.; Hershkowitz, D. (1998): Hadamard functions preserving nonnegative H-matrices *Linear Algebra and its Applications*,279:(1-3): 13-19.","frontiers":"Elsner, L., and Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications* 279, 13-19.","ieee":" L. Elsner and D. Hershkowitz, “Hadamard functions preserving nonnegative H-matrices”, *Linear Algebra and its Applications*, vol. 279, 1998, pp. 13-19.","bio1":"Elsner L, Hershkowitz D (1998)

Hadamard functions preserving nonnegative H-matrices.

Linear Algebra and its Applications 279(1-3): 13-19.","dgps":"Elsner, L. & Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications*, *279*(1-3), 13-19. ELSEVIER SCIENCE INC. doi:10.1016/S0024-3795(97)10094-5.

","ama":"Elsner L, Hershkowitz D. Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications*. 1998;279(1-3):13-19."},"article_type":"original","language":[{"iso":"eng"}],"intvolume":" 279","publisher":"ELSEVIER SCIENCE INC","publication_identifier":{"issn":["0024-3795"]},"publication_status":"published","author":[{"last_name":"Elsner","first_name":"Ludwig","full_name":"Elsner, Ludwig","id":"10509"},{"last_name":"Hershkowitz","first_name":"Daniel","full_name":"Hershkowitz, Daniel"}],"external_id":{"isi":["000075426400002"]},"status":"public","issue":"1-3","date_created":"2010-04-28T13:20:31Z","user_id":"67994","page":"13-19","year":"1998","type":"journal_article","quality_controlled":"1","publication":"Linear Algebra and its Applications","doi":"10.1016/S0024-3795(97)10094-5","department":[{"_id":"10020"}],"volume":279,"date_updated":"2019-07-08T13:58:30Z","isi":1,"keyword":["Hadamard matrix functions","H-matrices","spectral radius of nonnegative","matrices"],"title":"Hadamard functions preserving nonnegative H-matrices","abstract":[{"text":"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.","lang":"eng"}]}]