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The main result of this paper is the following: if A = (a(ij)) is an inverse M-matrix, A((r)) = (a(ij)(r)) denotes the rth Hadamard power of A, then A((r)) is again an inverse M-matrix for any real number r > 1. This settles a conjecture proposed by Wang et al. [B.Y. Wang, X.P. Zhang, F.Z. Zhang, On the Hadamard product of inverse M-matrices, Linear Algebra Appl. 305 (2000) 23-31] affirmatively. Naturally, it shows that the conjecture of Neumann [M. Neumann, A conjecture concerning the Hadamard product of inverses of M-matrices, Linear Algebra Appl. 285 (1998) 277-290] is also valid. (c) 2007 Elsevier Inc. All rights reserved.
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LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN: 0024-3795
Year: 2007
Issue: 2-3
Volume: 422
Page: 477-481
0 . 7 0 2
JCR@2007
1 . 0 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
JCR Journal Grade:2
Cited Count:
SCOPUS Cited Count: 9
ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 0
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