Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefininte matrices
Electronic Journal of Linear Algebra
Hadamard product, Nonnegative matrix, Positive semidefinite matrix, Positive definite matrix, Spectral radius, Kronecker product, Matrix inequality
X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius
Zhang, Fuzhen and Horn, Roger A., "Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefininte matrices" (2010). Mathematics Faculty Articles. 35.