[{"dini_type":"doc-type:article","abstract":[{"lang":"eng"}],"publication_status":"published","intvolume":" 279","keyword":[],"status":"public","dc":{"publisher":["ELSEVIER SCIENCE INC"],"identifier":["https://pub.uni-bielefeld.de/record/1625037"],"type":["info:eu-repo/semantics/article","doc-type:article","text"],"description":["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."],"language":["eng"],"creator":["Elsner, Ludwig","Hershkowitz, Daniel"],"rights":["info:eu-repo/semantics/closedAccess"],"title":["Hadamard functions preserving nonnegative H-matrices"],"subject":["Hadamard matrix functions","H-matrices","spectral radius of nonnegative","matrices"],"source":["Elsner L, Hershkowitz D. Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications*. 1998;279(1-3):13-19."],"relation":["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"],"date":["1998"]},"creator":{"id":"67994","login":"riedel"},"issue":"1-3","uri_base":"https://pub.uni-bielefeld.de","user_id":"67994","date_created":"2010-04-28T13:20:31Z","message":"NEWISI20100428 NEW ISI record:\r\nDepartments: Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany. --- Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel.\r\nISI Id: ISI:000075426400002","type":"journal_article","isi":1,"_id":"1625037","_version":8,"date_updated":"2019-07-08T13:58:30Z","external_id":{"isi":[]},"page":"13-19","author":[{"last_name":"Elsner","id":"10509","first_name":"Ludwig"},{"last_name":"Hershkowitz","first_name":"Daniel"}],"language":[{}],"quality_controlled":"1","citation":{"bio1":"Elsner L, Hershkowitz D (1998)

Hadamard functions preserving nonnegative H-matrices.

Linear Algebra and its Applications 279(1-3): 13-19.","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

","ieee":" L. Elsner and D. Hershkowitz, “Hadamard functions preserving nonnegative H-matrices”, *Linear Algebra and its Applications*, vol. 279, 1998, pp. 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.","mla":"Elsner, Ludwig, and Hershkowitz, Daniel. “Hadamard functions preserving nonnegative H-matrices”. *Linear Algebra and its Applications* 279.1-3 (1998): 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.

","angewandte-chemie":"L. Elsner, and D. Hershkowitz, “Hadamard functions preserving nonnegative H-matrices”, *Linear Algebra and its Applications*, **1998**, *279*, 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","harvard1":"Elsner, L., & Hershkowitz, D., 1998. Hadamard functions preserving nonnegative H-matrices. *Linear Algebra and its Applications*, 279(1-3), p 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.","lncs":" Elsner, L., Hershkowitz, D.: Hadamard functions preserving nonnegative H-matrices. Linear Algebra and its Applications. 279, 13-19 (1998)."},"volume":279,"publication_identifier":{"issn":[]},"publication":"Linear Algebra and its Applications","department":[{"tree":[{"_id":"10020"}],"_id":"10020"}],"article_type":"original"}]