Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

• Jing Li
• Guang Zhou

• Hadamard product
• Fan product; nonnegative matrix
• M-matrix
• Spectral radius
• Minimum eigenvalue
• 1-path cover.

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