On the spectral radius and the spectral norm of Hadamard products of nonnegative matrices

✍ Scribed by Zejun Huang

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 140 KB
• Volume: 434
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.08.038

✦ Synopsis

We prove the spectral radius inequality ρ(A

for nonnegative matrices using the ideas of Horn and Zhang. We obtain the inequality A • B ρ(A T B) for nonnegative matrices, which improves Schur's classical inequality

, where • denotes the spectral norm. We also give counterexamples to two conjectures about the Hadamard product.