Open Access
2015 On the spectral radius of Hadamard products of nonnegative matrices
Dongjun Chen, Yun Zhang
Banach J. Math. Anal. 9(2): 127-133 (2015). DOI: 10.15352/bjma/09-2-10


We present some spectral radius inequalities for nonnegative matrices. Using the ideas of Audenaert, we then prove the inequality which may be regarded as a Cauchy--Schwarz inequality for spectral radius of nonnegative matrices $$ \rho(A \circ B) \leq [\rho(A \circ A)]^{\frac{1}{2}}[\rho(B\circ B)]^{\frac{1}{2}}. $$ In addition, new proofs of some related results due to Horn and Zhang, Huang are also given. Finally, we interpolate Huang's inequality by proving $$ \rho(A_{1}\circ A_{2} \circ \cdots \circ A_{k}) \leq [\rho(A_{1}A_2\cdots A_{k})]^{1-\frac{2}{k}}[\rho((A_{1}\circ A_{1})\cdots (A_{k}\circ A_{k})]^{\frac{1}{k}} \leq \rho(A_{1}A_2 \cdots A_{k}).$$


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Dongjun Chen. Yun Zhang. "On the spectral radius of Hadamard products of nonnegative matrices." Banach J. Math. Anal. 9 (2) 127 - 133, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1314.15008
MathSciNet: MR3296110
Digital Object Identifier: 10.15352/bjma/09-2-10

Primary: 15A18‎
Secondary: 47A10 , 47B37

Keywords: Hadamard product , nonnegative matrices , spectral radius

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 2 • 2015
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