Spectral radius of Hadamard product versus conventional product for non-negative matrices

Details Spectral radius of Hadamard product versus conventional product for non-negative matrices Spectral radius of Hadamard product versus conventional product for non-negative matrices

2009-07-19

arxiv.org/abs/0907.3312v1

Lin. Alg. Appl., 432(1), 366-368 (2010)

Mathematics

Functional Analysis

4.1 pages

Scientific paper

We prove an inequality for the spectral radius of products of non-negative
matrices conjectured by X. Zhan. We show that for all $n\times n$ non-negative
matrices $A$ and $B$, $\rho(A\circ B)\le\rho((A\circ A)(B\circ
B))^{1/2}\le\rho(AB)$, where $\circ$ represents the Hadamard product.

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