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