On the spectral radius and the spectral norm of Hadamard products of nonnegative matrices |
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Authors: | Zejun Huang |
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Institution: | Department of Mathematics, East China Normal University, Shanghai 200241, China |
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Abstract: | We prove the spectral radius inequality ρ(A1°A2°?°Ak)?ρ(A1A2?Ak) for nonnegative matrices using the ideas of Horn and Zhang. We obtain the inequality ‖A°B‖?ρ(ATB) for nonnegative matrices, which improves Schur’s classical inequality ‖A°B‖?‖A‖‖B‖, where ‖·‖ denotes the spectral norm. We also give counterexamples to two conjectures about the Hadamard product. |
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Keywords: | 15A42 15A60 15A69 |
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