---
_id: '1625037'
abstract:
- lang: eng
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.'
article_type: original
author:
- first_name: Ludwig
full_name: Elsner, Ludwig
id: '10509'
last_name: Elsner
- first_name: Daniel
full_name: Hershkowitz, Daniel
last_name: Hershkowitz
citation:
ama: Elsner L, Hershkowitz D. Hadamard functions preserving nonnegative H-matrices.
*Linear Algebra and its Applications*. 1998;279(1-3):13-19.
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
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

bio1: 'Elsner L, Hershkowitz D (1998)

Hadamard functions preserving nonnegative
H-matrices.

Linear Algebra and its Applications 279(1-3): 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.'
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.

frontiers: Elsner, L., and Hershkowitz, D. (1998). Hadamard functions preserving
nonnegative H-matrices. *Linear Algebra and its Applications* 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.
ieee: ' L. Elsner and D. Hershkowitz, “Hadamard functions preserving nonnegative
H-matrices”, *Linear Algebra and its Applications*, vol. 279, 1998, pp.
13-19.'
lncs: ' Elsner, L., Hershkowitz, D.: Hadamard functions preserving nonnegative H-matrices.
Linear Algebra and its Applications. 279, 13-19 (1998).'
mla: 'Elsner, Ludwig, and Hershkowitz, Daniel. “Hadamard functions preserving nonnegative
H-matrices”. *Linear Algebra and its Applications* 279.1-3 (1998): 13-19.'
wels: 'Elsner, L.; Hershkowitz, D. (1998): Hadamard functions preserving nonnegative
H-matrices *Linear Algebra and its Applications*,279:(1-3): 13-19.'
date_created: 2010-04-28T13:20:31Z
date_updated: 2019-07-08T13:58:30Z
department:
- _id: '10020'
doi: 10.1016/S0024-3795(97)10094-5
external_id:
isi:
- '000075426400002'
intvolume: ' 279'
isi: 1
issue: 1-3
keyword:
- Hadamard matrix functions
- H-matrices
- spectral radius of nonnegative
- matrices
language:
- iso: eng
page: 13-19
publication: Linear Algebra and its Applications
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: ELSEVIER SCIENCE INC
quality_controlled: '1'
status: public
title: Hadamard functions preserving nonnegative H-matrices
type: journal_article
user_id: '67994'
volume: 279
year: '1998'
...