---
res:
bibo_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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Ludwig
foaf_name: Elsner, Ludwig
foaf_surname: Elsner
foaf_workInfoHomepage: http://www.librecat.org/personId=10509
- foaf_Person:
foaf_givenName: Daniel
foaf_name: Hershkowitz, Daniel
foaf_surname: Hershkowitz
bibo_doi: 10.1016/S0024-3795(97)10094-5
bibo_issue: 1-3
bibo_volume: 279
dct_date: 1998^xs_gYear
dct_identifier:
- UT:000075426400002
dct_isPartOf:
- http://id.crossref.org/issn/0024-3795
dct_language: eng
dct_publisher: ELSEVIER SCIENCE INC@
dct_subject:
- Hadamard matrix functions
- H-matrices
- spectral radius of nonnegative
- matrices
dct_title: Hadamard functions preserving nonnegative H-matrices@
...