Some new bounds on the spectral radius of matrices

A new lower bound on the smallest eigenvalue tau(A * B) for the Fan product of two nonsingular M-matrices A and B is given. Meanwhile, we also obtain a new upper bound on the spectral radius rho(A o B) for nonnegative matrices A and B. These bounds improve some results of Huang (2008) [R. Huang, Some inequalities for the Hadamard product and the Fan product of matrices, Linear Algebra Appl. 428 (2008) 1551-1559]. Crown Copyright (C) 2009 Published by Elsevier Inc. All rights reserved.