Hadamard functions preserving nonnegative H-matrices

Elsner L, Hershkowitz D (1998)
Linear Algebra and its Applications 279(1-3): 13-19.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Elsner, LudwigUniBi; Hershkowitz, Daniel
Abstract / Bemerkung
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.
Stichworte
Hadamard matrix functions; H-matrices; spectral radius of nonnegative; matrices
Erscheinungsjahr
1998
Zeitschriftentitel
Linear Algebra and its Applications
Band
279
Ausgabe
1-3
Seite(n)
13-19
ISSN
0024-3795
Page URI
https://pub.uni-bielefeld.de/record/1625037

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Elsner L, Hershkowitz D. Hadamard functions preserving nonnegative H-matrices. Linear Algebra and its Applications. 1998;279(1-3):13-19.
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
Elsner, L., and Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. Linear Algebra and its Applications 279, 13-19.
Elsner, L., & Hershkowitz, D., 1998. Hadamard functions preserving nonnegative H-matrices. Linear Algebra and its Applications, 279(1-3), p 13-19.
L. Elsner and D. Hershkowitz, “Hadamard functions preserving nonnegative H-matrices”, Linear Algebra and its Applications, vol. 279, 1998, pp. 13-19.
Elsner, L., Hershkowitz, D.: Hadamard functions preserving nonnegative H-matrices. Linear Algebra and its Applications. 279, 13-19 (1998).
Elsner, Ludwig, and Hershkowitz, Daniel. “Hadamard functions preserving nonnegative H-matrices”. Linear Algebra and its Applications 279.1-3 (1998): 13-19.