Abstract: Using Brauer’s theorem and sequences of upper bounds of the elements of inverse matrices, the author gave a monotone nonincreasing sequences of upper bounds of the spectral radius ρ(B·A^-1) for the Hadamard product of the inverse matrix A^-1 of a nonsingular Mmatrix A and a nonnegative
matrix B and gave some monotone nondecreasing sequences of lower bounds for the minimum eigenvalue τ(A) of Aby using this sequences of upper bounds. The obtained results were verified by several numerical examples. Numerical results show that these obtained estimates are more accurate than some existing results.

Key words: nonnegative matrix, M-matrix, minimum eigenvalue, Hadamard product, spectral radius