Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 432, Issue 1, Pages 366-368Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2009.08.017
Keywords
Spectral radius; Hadamard product; Non-negative matrix; Matrix inequality
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We prove an inequality for the spectral radius of products of non-negative matrices conjectured by Zhan. We show that for all n x n non-negative matrices A and B, rho(A circle B) <= rho(A circle A)(B circle B))(1/2) <= rho(AB), in which circle represents the Hadamard product. (C) 2009 Elsevier Inc. All rights reserved.
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