article
Hadamard functions preserving nonnegative H-matrices
published
yes
Ludwig
Elsner
author 10509
Daniel
Hershkowitz
author
10020
department
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 INC1998
eng
Hadamard matrix functionsH-matricesspectral radius of nonnegativematrices
Linear Algebra and its Applications
0024-3795
00007542640000210.1016/S0024-3795(97)10094-5
2791-313-19
Elsner L, Hershkowitz D (1998) <br /><em>Linear Algebra and its Applications</em> 279(1-3): 13-19.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Elsner, L. & Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. <em>Linear Algebra and its Applications</em>, <em>279</em>(1-3), 13-19. ELSEVIER SCIENCE INC. doi:10.1016/S0024-3795(97)10094-5.</div>
Elsner, L., and Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. <em>Linear Algebra and its Applications</em> 279, 13-19.
L. Elsner and D. Hershkowitz, “Hadamard functions preserving nonnegative H-matrices”, <em>Linear Algebra and its Applications</em>, vol. 279, 1998, pp. 13-19.
Elsner, L., & Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. <em>Linear Algebra and its Applications</em>, <em>279</em>(1-3), 13-19. doi:10.1016/S0024-3795(97)10094-5
Elsner, L., Hershkowitz, D.: Hadamard functions preserving nonnegative H-matrices. Linear Algebra and its Applications. 279, 13-19 (1998).
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Elsner, L., & Hershkowitz, D. (1998). Hadamard functions preserving nonnegative H-matrices. <em>Linear Algebra and its Applications</em>, <em>279</em>(1-3), 13-19. doi:10.1016/S0024-3795(97)10094-5</div>
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Elsner, Ludwig, and Hershkowitz, Daniel. 1998. “Hadamard functions preserving nonnegative H-matrices”. <em>Linear Algebra and its Applications</em> 279 (1-3): 13-19.</div>
Elsner, L.; Hershkowitz, D. (1998): Hadamard functions preserving nonnegative H-matrices <em>Linear Algebra and its Applications</em>,279:(1-3): 13-19.
L. Elsner, and D. Hershkowitz, “Hadamard functions preserving nonnegative H-matrices”, <em>Linear Algebra and its Applications</em>, <strong>1998</strong>, <em>279</em>, 13-19.
Elsner, Ludwig, and Hershkowitz, Daniel. “Hadamard functions preserving nonnegative H-matrices”. <em>Linear Algebra and its Applications</em> 279.1-3 (1998): 13-19.
Elsner L, Hershkowitz D. Hadamard functions preserving nonnegative H-matrices. <em>Linear Algebra and its Applications</em>. 1998;279(1-3):13-19.
Elsner, L., & Hershkowitz, D., 1998. Hadamard functions preserving nonnegative H-matrices. <em>Linear Algebra and its Applications</em>, 279(1-3), p 13-19.
Elsner L, Hershkowitz D (1998) <br />Hadamard functions preserving nonnegative H-matrices.<br />Linear Algebra and its Applications 279(1-3): 13-19.
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