# Spectral radius of Hadamard product versus conventional product for non-negative matrices - Mathematics > Functional Analysis

Abstract: We prove an inequality for the spectral radius of products of non-negativematrices conjectured by X. Zhan. We show that for all $n\times n$ non-negativematrices $A$ and $B$, $hoA\circ B\le hoA\circ AB\circB^{1-2}\le hoAB$, where $\circ$ represents the Hadamard product.