Abstract: This paper found a new type upper bound of ρ(A。B) which was the spectral radius of the Hadamard product of two nonnegative matrices A and B by using Cauchy—Schwitz inequality and compared the new type upper bound with the classical results. In the same way, this paper found a new type lower bound of т(A★B),which was the minimum eigenvalue of the Fan product of two M--matrices A and B.

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