Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Abstract

In this paper, an upper bound on the spectral radius ρ ( A ∘ B ) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ ( C ★ D ) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results.

Keywords

• Hadamard product
• nonnegative matrices
• spectral radius
• fan product
• <i>M</i>-matrix
• inverse <i>M</i>-matrix
• minimum eigenvalue